most bathroom extractors fit a 4" hole in the wall (usually a 110mm plastic duct) and are interchangable. There are some that go in the loft above the bathroom ceiling (of which some are very powerful) and still a few that are recessed into the wall. The minimum extraction rate of the weakest fans is usually about 80 cubic metres per hour (nominal). The extract rate is usually shown in the advert or on the packaging. You can browse some extractor fans here
Some have a timer, which needs an extra wire from the switch, which will already be present if your old fan works that way.
People talk inaccurately about Part P.
All Electrical work is supposed to be done to standard and a certificate issued. Some work is not obliged to be notified under Building Regulations.
Approved Document Part P is about electrical safety and applies to everything in or attached to a dwelling or associated buildings, gardens etc.
Schedule 4 of the Building Regulations defines what is not notifiable.
You read through this to see if any of the clauses apply to what you are doing. If and when you reach one that does, you stop reading, because the work is not notifiable. If none of the clauses cover the work, it is notifiable. There are two routes to notify; one is to submit plans to your local authoriy's Building Control Office, pay their fees, fill in their forms, get their approval and follow their processes; the other, which is usually easier and cheaper, is to engage a contractor who is a member of a Competent Persons Scheme and is authorised to submit his own documents. It is your responsibility to ensure that he does. You might make it a condition of paying his bill. As Andrex say, a job isn't finished until the paperwork is done.
Removing a faulty old extractor and replacing it with a new one appears to me to fall within 1(a) of Schedule 4 so is not notifiable. However it still has to be done under the rules of Part P. One way of satisfying Part P is to carry out the work to the regulations of a body such as the Institution of Engineering and Technology (formerly the Institute of Electrical Engineers) which are also British Standard BS 7671. These are propagated in numerous training courses, handbooks and guides, and a Competent Person will (should) be fully familiar with them, and able to look them up in case of doubt. If he chooses to carry it out in some different way, he may be called upon to prove that his alternative method met the safety requirements of Part P, for example, in court following a fatal accident. Electricians usually prefer to avoid this.
This is in England and Wales. Scotland has some differences