10 gallons would be fine for a 75 if all you are doing is using it as a place to store your heater and skimmer. might i suggest if you are going to be able to hide the sump away to instead use a rubbermaid container and save yourself a little bit of money (that is of course unless you weere planning on using your existing 10 glass). you will have a bit more flexibility for the future.
the skimmer should be fine. if you eventually decide to run a fuge (highly recommended) the skimmer will become less important as most of your nutrient absorption will come in the form of algae growth.
as for the dimensions, i like the sounds of that tank, although it does seem a bit long for a dorm room (hope you arent going to be trying to fit one of those bad boys in there).
the rest of the stuff sounds good. on a 300 gph overflow, you might want to bolster your in tank water flow by adding on a closed loop, or you can look into getting a overflow that will let you do a bit more turnover, say 500 to 600 gph. on a 60" tank though you can do a closed loop for pretty cheap, which will allow you to route water to both ends of the tank and work around any major rock features. if you can get a good deal on a mag 5 or something on ---- (i have seen them for around 35 bucks) that would be a very viable option. the only cost on top of that is some pipe and fittings, probably another 20 bucks or so, and that way you will not be pushing a ton of water through a 10 gallon sump. ballpark figure that most people shoot for is 10X your volume per hour, which is why i suggest either a larger flow overflow or the closed loop system.
if you want to save a bit of cash, as this is probably starting to push your original budget, you can get your initial 50 lbs of live rock or whatever you had decided on, and then bulk it out with some dry baserock. it will give you more rock to play with as far as structure building goes, and it will in time become seeded by the rest of your live rock, acting just as effeciently in terms of filtration.
here is a pic of my tank. it is a 29 with about 70 lbs of rock for reference. being a 29, it is the same front to back as your standard show 55, and it is pretty much full front to back, with maybe 2 to 3" of exposed sand in front of the wall. incidentally, more than half of this rock is aforementioned dry baserock that i added about a month ago.