As students, most people go out on Broad St, often after having a few drinks in Selly Oak first.
Risa - This is the place to be on a Monday night. Must be a student to get in. Drinks are actually reasonably priced, but it probably still pays to get pissed at uni beforehand!
Bobby Browns - This is my favourite club and on a a Wednesday it's awesome. It's set out in several smallish sized rooms. They've started doing Vodbull nights there too (double V/RB for £1!). Great student atmosphere. The main place to go on a Wednesday.
The Works - Wednesday is also a student night there. This place is one huge room (with a smaller one upstairs). In my opinion, not as good as Bobby's, but it may suit some people more.
Until it got closed down, Zanzibar (not on Broad St, but in the Chinese Quarter) was the place to go on a Thursday for its legendary vodbull nights. Now these nights are being held at various other places around town. There's also clubs like Dome and Polaris, but I don't think these are as good as those above.
Then there are the bars like Reflex, Lloyds, Whetherspoons, Rococo, Revolution, Yates and Flares (70s club! Classic!) where you can go if you're looking for something with a little less student atmosphere. These places are cheaper and have some really good drinks bargains going on. There are other places off Broad St - MedBar is a good one in Digbeth, even if it is a little grungy.
So that's Broad St in a nutshell. I know I haven't mentioned all the places, but these are the ones that I go to, and the ones that most other students go to. As for price, it really does vary. You'll find yourself doing it the cheap way - either by necking a bottle of vodka beforehand, or going to Reflex and getting those £1 pints/bottles during week nights.
Oh, and one last thing. Do not miss the £5 all-you-can-drink night at the Underground in the Guild that they'll put on in the second term. And I do mean all you can drink. I'll never forget that night!
Anyway, hope this helps.