Obviously the two main categories of mediumistic phenomena Physical & Intelligent directly correspond to two main types of mediums:

Physical Mediums: Mediums who have a tendency to physical manifestations of Spirit communications through the giving of ectoplasm.

Intellectual Mediums: Mediums who have a tendency to intellectual manifestations of Spirit communications through the bonding of perispirits.

(The Mediums Book Chapter 16 #187 – #188

Other main types of mediums:

Sensitive Mediums: Persons who feel the presence of spirits by a peculiar impression, general or local, vague or undecided. Most of these distinguish good or evil spirits by the nature of the impression caused by them.

Natural or Unconscious Mediums: Those who call forth the phenomena spontaneously, without any action of their will, and for the most part unconsciously.

Voluntary Mediums: Those who have the power of calling forth the phenomena at their will (though they are ineffective if the Spirits are unwilling to cooperate).

A special category of mediumship are those based on level of development:
The Mediums’ Book Chapter 14 #192

Novice mediums: those whose medianimic faculty is not yet completely developed, and who lack experience.

Unproductive mediums: those who obtain only insignificant results, such as monosyllables, letters, or mere strokes (See Chap. XVI I. Formation of mediums).

Fully formed mediums: those whose medianimic faculties are completely developed, and who transmit spirit-communications easily, quickly, and without hesitation. It is evident that this perfection cannot be obtained without practice ; in the case of novice mediums, the transmission is usually slow and difficult.

Laconic mediums: those who, though easily influenced, obtain only short and undeveloped communications.

Explicit mediums: the communications obtained by these mediums have all the length and amplitude that could be arrived at by a writer of first-rate ability. “This aptitude depends upon the expansibility and facility of combination of the fluids required. Spirits seek for mediums of this nature, for treating of subjects which demand full development.”

Experienced mediums: facility of writing, drawing, etc, is a result of habit, and is often quickly acquired; while experience is the result of a serious study of all the difficulties of practical Spiritism. Experience gives to the medium the tact necessary for judging of the quality of the spirits who manifest themselves, ascertaining their good or bad qualities, and discovering the tricks of deceptive spirits who falsely assume the appearances of truth. The importance of this quality is easily understood, for, without it, all others are useless. Unfortunately, many mediums confound experience, the fruit of study, with aptitude, the result of organisation, and fancy themselves to be perfect, because they write with facility; they often reject counsel, and become the prey of hypocritical and lying spirits, who lay hold of them by flattering their vanity (See Chap. XXIII. Obsession).

Flexible mediums: those whose faculty enables them to lend themselves with great facility to a great diversity of communications, and through whom, all spirits, or nearly all, are able to manifest themselves, spontaneously, or in response to evocation. “This variety of mediums differs but slightly from sensitive mediums.”

Exclusive mediums: those through whom one spirit manifests him/herself to the exclusion of all others, and answers for all the other spirits that may be called for through the intervention of the medium. “Such exclusiveness is always the result of defective flexibility on the part of the medium. A good spirit may attach him/hermself to a medium from sympathy, and for a laudable end; but, when the spirit is an evil one, he/she does this invariably with the view of keeping the medium dependent upon him. Such exclusiveness should be avoided, as it borders too closely on obsession ” (See Chap. XXIII. Obsession).

Mediums for evocations: flexible mediums are naturally the fittest for obtaining this kind of manifestation, and for queries of detail that may be addressed to spirits. “The answers of such mediums are almost always confined within a very narrow compass, incompatible with the treatment of general subjects.”

Mediums who receive spontaneous communications: they are used for the transmission of information spontaneously given by spirits who come without having been evoked. It is always difficult, and often impossible, to make the evocation of any given spirit through mediums in whom this aptitude exists as a special faculty. “Nevertheless, these are better provided with medianimic tools than the mediums previously named. This expression, provided with tools refers to brain-material, for a larger amount of intelligence on the part of the medium is needed for spontaneous dictation than for evocations. By ‘spontaneous dictation’ I mean communications worthy of the name, and not mere fragmentary sentences, or a few commonplace thoughts such as may be found in all human heads.

Another special category within types of mediums are those which reflects the ethical evolution and lack of ethical evolution of the medium.

The Mediums Book Chapter 15 # 196-197

Imperfect Mediums.

Mediums who are obsessed: those who cannot rid themselves of importunate, deceptive spirits, but who are fully aware of; and regret, this obsession.

Fascinated mediums: those who are acted upon by deceptive spirits, but who are not aware of this obsession, and who are consequently under a delusion as to the nature of the communications they receive.

Subjugated mediums: those who are under the moral, and sometimes the physical, domination of evil spirits.

Frivolous mediums: those who do not regard their faculty in a serious light, and who exercise it only for amusement or for futile objects.

Careless mediums: those who derive no moral profit from the instructions which they receive, and whose conduct and habits are not improved thereby. Presumptuous mediums; those who assume themselves to be the only ones who are in communication with superior spirits. They believe themselves to be infallible, and regard as worthless and erroneous whatever does not come through themselves.

Presumptuous mediums: those who feed their vanity with the communications which they receive, imagine themselves to have nothing more to learn in regard to Spiritism, and do not apply to themselves the lessons often read to them by spirits. Not contented with the medianimic faculties they possess, they imagine themselves to possess all the others.

Touchy mediums: they are a variety of the proud ones, and are hurt at the criticisms of which they are the object; they take offence at the slightest contradiction, and, if they show what they obtain, they do so in order to be admired, and not at all to profit by the opinion of the listeners. They generally take an aversion to those who do not applaud them unreservedly, and desert the meetings in which they cannot take a leading part.

Mercenary mediums: those who make their faculty a source of pecuniary gain.

Ambitious mediums: those who, without putting a price upon the exercise of their faculty, seek to turn it to their own advantage, social, or other.

Dishonest mediums: those who, possessing some genuine medianimic faculties, simulate others which they do not possess, in order to give themselves importance.

Selfish mediums: those who use their faculty only for personal ends, and who keep to themselves the communications they receive.

Jealous mediums: those who are vexed at seeing other mediums better developed, and more highly appreciated, than themselves. All these bad qualities of mediums have necessarily their counterparts in good ones.

Good Mediums.

Serious mediums: those who only use their faculties for good and really useful ends, and who would regard it as a profanation to use them for the satisfaction of the curious and indifferent, or for any futile purpose.

Modest mediums; those who make no merit of the communications they receive, however good they may be. They look upon themselves as being only the instruments of others, and do not regard themselves as infallible. Far from shunning disinterested counsel, in regard to the exercise of their medianimity, they seek it.

Devoted mediums: those who understand that the true medium has a mission to fulfill, and that he/she must be ready, when necessary, to sacrifice his/her tastes, habits, pleasure, time, and even his/her worldly interests, to the good of others.

Safe mediums: those who, in addition to their power, are worthy of confidence on account of their personal excellence and the elevated nature of the spirits who assist them, and who are thus the least likely to be deceived. We shall see hereafter that this security does not depend in any way upon the honorability of the names assumed by the communicating spirits.