What you described is a sump. That is indeed a pain in the butt, especially for a beginner. It's also completely unnecessary for a freshwater tank, as it's mostly used for saltwater tanks.
A canister filter sits under the stand, with hoses running up to plastic (or glass) tubes that hang over the edge into the aquarium. The water goes in one pipe, down a tube, through the filter, than back up another hose and though a pipe into the aquarium. They are very easy to set up, zero drilling required.
Here is an example of a very small canister filter on a 5 gallon tank for reference...
Credit to Chase127 on here.
These things literally take ten minutes to install. No tools needed.
As far as price goes... get out of petsmart, and start looking online! Petsmart is fine for buying the tank and stand, but their prices on equipment is not great. check out big al's, foster and smith, thatpetplace. You can pick up an eheim 2217 for $140 shipped on big als.The 2217 is an amazing filter, it works great and is uber-reliable.
but if you wanted 2 canisters, you might want to check out the Sun Sun filters. they are basically a cheaper chinese filter, but supposedly are working quite well for lots of people on here. Here is a link to a thread reviewing them.
Finally... xmas' idea isn't a bad one. Have you thought about getting a smaller tank and really getting a feel for the hobby before you invest in a big set-up? A 20 gallon high or a 40 gallon breeder are good starter tanks to make lots of mistakes with, (you will make mistakes, we all do) and they are easier to maintain and correct problems in.
That said, if your heart is set on a 75 gallon, by all means get it. Especially if you have an understanding mother... as you get older, you might find girlfriends/wives have a much lower tolerance for that much water in their house.