I've only got about $150 to spend each month (study grant), $40 of which I use to pay my internet, and a gym card costs $45/month,
Do you live in the world's most expensive town? Who in hell pays that for internet, especially as a student? Get a new ISP, it shouldn't be chewing up a third of you allowance. As someone else mentioned that's also an impractical amount to pay out for gym membership which leads us to:
If you can't join a cheap eg subsidised college gym with basic free weights (you have cardio covered with the cycling at home) then buy the best bench (preferably with integrated squat rack) with a barbell, dumbells and as much weight in decent divisions (ie more 10kg, 5 plates rather than loads of 2.5 and 1.5 plates that cheap sets often come with). At 132 pounds you won't b edoing mega lifts for a while so you dont' need to buy excessive plates at this stage.
Millions of people take up weights and join gyms, but millions also give up so hedge your bets ie if you join a gym you might be comiites for a 1 year membership which will sting if you don't keep it up, weights you can at least re-sell. The other upside of this is that you should be able to buy weights second hand off some other optimistic "get buff for summer" mug who has done nothing but stub his toe on them for the last year. Put an ad on the notice board or get them off ebay etc.
To gain the most muscle focus on the lifts that exercise the most muscle (in priority order):
1) Squats or leg press
2) Deadlifts
3) Bench or dips
4) Military press
5) Weighted chinups, pulldowns, or rows
Sounds about right but I would do Bench rather than Dips initially and don't worry about weighting you chins at first until you get used to them and build a bit of technique. Do all movements slowly otherwise you'll be training your connective tissue more than your muscles.
For the first couple of months just do the above exercises for 4 sets each, 1st set at a weight you can do 12 for then up the weight for the next 3 sets you can do 8-10 reps on. Rest 2 minutes between sets, so should take c60 mins for a full body workout which you should do every 4 days at first. You can up the frequency and lower the reps once your body (Muscles, Tendons, CNS etc) has adjusted to the initial culture shock.
Before people jump on me with "reps too high" and split systems etc, I am keeping this simple, easy to understand (I hope) and not so hardcore that's it's going to burn someone out/be time-impractical/cause an injury. This guy is just starting out and is not built like a barn.
I have been upping my food intake, as well (about 2100 (weekends, 3 major meals/day) to 2500 (school days, 4 major meals/day) kcal/day now, with more lean meat, as well as lots of whole-grain food (which I already ate before) for breakfast and supper), and no snacks, sodas, french fries etc. whatsoever. I do eat some red meat, though, but that's because I live with my parents and I don't cook my own food. If I had the option, I would eat something else instead
Fine, try and keep it to the 2500 end whilst focussing, as you are, on quality protein and complex carbs with moderate fat.
If you're still at it in 2 months report back and let us know if you have made any progress and/or need a more advanced approach.