My computer that I bought a few months ago has similar stats:
Some asus motherboard, I'm not sure which one.
AMD Phenom II x4 965 Processor 3.4GHz
ATI Radeon HD5670 1GB
1TB Serial ATA-II HD
I can stream in hd. I also have 5 mbps upload which is a huge reason why. But I can stream with no performance issues. I think you should find out your upload speed though, it's going to be very important.
I can run ultra at about 35-40 fps. Not perfect, but playable. I wouldn't try to play/stream on ultra. I always play low just as matter of preference.
I'd look on amazon just for the hell of it because as a student there's free Amazon Prime and you can avoid paying sales tax. Tax+shipping on a new computer can run hundreds.
Lastly if it's anything like mine the fans are pretty damn loud. Something to consider if you don't have your own room or whatever.
ZvT is by far the easiest match up for me, but perhaps it's cause the Ts ive been playing (2.8ish k diamond level) all seem to suck.
I'm only silver (should be gold soon), but it's the easiest matchup for me as well. So many of them can't handle muta harass or they build a ridiculous amount of turrets and I can just grab a couple more expos. Too many of them build stupid units like vikings, banshees or try to drop me when they know I have mutas and not enough of them use siege tanks.
Someone should really start a site that sells replays. You could compensate masters level players for sharing their ladder replays and then give access to them for a monthly fee or sell them in packs or something. I'm sick of how everything is on streams or youtube commentaries, because I like directing the camera and studying builds in as much detail as I want.