For now you are fine with using the undergravel filter. When you moved the tank it was probably pretty gross and got a lot of the gunk out from under the UGF plates under the gravel right? Generally with UGF's you want to change the airstones whenever you notice fewer bubbles coming out.
If I were you I would set the tank up and run it as the old owner suggests (since its probably cycled and everything is good to go with the gravel etc), do your gravel cleaning/ water changes once a week and do some research on canister filters, take a look at what would suit your setup and prices, then get the one(s) you like and get them set up. After you've run the ugf with the canister filter(s) for a month or so you should be fine to take your fish out and do an overhaul on the tank, taking out the UGF plates and cleaning.