Rightmove.co.uk is a great site for looking for properties, and it also lets you view properties on a map, so if you know the general area you want to be in but don't know the postcode (or if the nicer area is only a small fraction of a postcode >_>) you can easily find places in an area you want. That should help you get an idea of prices too - i don't know what theyre like in glasgow. In edinburgh you can find a decent place fairly central (certainly in a studenty area) for anywhere from £500-1000 dependant on size, bedrooms, etc.
The types of flats vary. in edinburgh there are buildings called tenements, but theyre not a negative thing that the word implies in the US, just buildings with flats in. If you google tenements edinburgh you can see some examples. Studios, 1bdrm, 2 bdrm, and some places have large 4-5 bedroom flats which groups of students may all let together and flat share. There are also some newer apartment buildings that are a bit more modern and perhaps more like apartment conmplexes you might be familiar with. If you go out of the city centre or close to the vet school campus you could rent a little terraced house or the upper floor of a small semidetached house etc.
@DVMDream were you paying cost of the phone itself in your monthly phone bill? 😵 i only pay £20 a month for phone, but im not paying for the cost of the mobile.