Getting a cycling saddle that fits
Essentially you have one of these:



This is an older type of saddle clamp that was popular when seat posts were made from steel rather than alloy. Any saddle bought from a bike shop will fit. The general idea is that the bolt goes behind instead of in front of the post, you tighten it up on both sides so that the top of the seat is level and the seat is centered on the rails. Swapping over a seat can be a 'bit of a fiddle' as there isn't necessarily a lot of room under the seat to assemble all the bits and keep them in place whilst you do up the bolt.

As for saddle choice, you don't have to worry about weight, the elements or the seat getting damaged from being in accidents etc. Therefore you should be able to choose from the heavier/more comfortable seats to find something in budget.