When you say you bought 10 new filters, you mean the replacement cartridges? Long term you could potentially save quite a bit of money by switching filter types. I strongly recommend the Hagen power filters. You can choose which media you put in, meaning you can skip carbon altogether (if you want) and then you don't have to worry about replacing filter media once a month. Instead you would just wash out one part (sponge or ceramics) in old tank water. You would need to baffle this filter, but I have found that taking one of the sponges meant for the inside of the filter and rubber banding it to the front works wonders. My water is actually too still for my liking.
Of course you don't have
to get a new filter. You could use your old one for now and just supplement with more water changes. The same thing goes for the gravel. It is not needed, it is something we put in to make the tank look better for us. Yes, it can help with an established tank in that it does provide a place for more beneficial bacteria to grow, but you don't need it. You could easily use whatever you have for now.
So that means the only thing you absolutely need is a heater. I can't be much help on recommending any particular brands because I get all of my heaters second hand. Just make sure it is adjustable. I don't like preset much, and on anything bigger than 5 gallons you really should get something you can set.
Does the tank come with a light? Again, this is something we use to appreciate the fish, and could be supplemented with a desk lamp.
You could also divide the tank.... Then you could have your two 2.5s at home and the 10 gallon divided at college. 10s are great to divide, but that is just me being a betta addict...