They ll be around the same price amp; they will also be used nightly. (Except the couch would be used daily) $300 - $450
I'd buy a good twin bed and put it against one wall in the corner with lots of decorative pillows so I could use it as a sofa. There is not a sofa bed made for any price that is as comfy as a regular bed.
By a bed to have a comfortable night sleep. Then save up for a sofa set
don't under any circumstances buy a sleeper sofa. they make a crappy sofa and and even crappier bed... the worst of both. and you'll hate having to unmake it every single day to put it back into a couch. you do know that you have to strip the sheets and blankets off in order to put the frame back inside to use it as a couch right? if you can only afford on thing right now then buy a 7' - 9' long sofa. that way you can sleep on it for a while until you get a few more bucks to get yourself a bed.
One of my best night's sleep ever - I remember it to this day, 10 years later - was on an opened futon. However, I have never spent a great night on a sleeper sofa. I had a very good one - it cost $900 in 1991 - and even it wasn't fabulous. It improved markedly when I added secondary supports that I would install whenever we opened it up. Spend your money on a good bed first. You need sleep more than anything else, and you can save up for a sofa.
You can't but any kind of decent sleeper sofa for $450. The best you could hope for would be a futon type of thing. We slept on a good quality sofa sleeper for a few years, and they are not good beds if you want a comfortable mattress. If you get a sleeper sofa, you also have to deal with the bedding every single time you convert it from sofa to bed. I would buy a new bed and maybe look for a used sofa, if you need both.