You definitely want more kegs than taps, so you don't need to wait for a keg to drain before packaging another brew.
When you say regulator, I would think the kegerator would come with one as the kegerator can't be used without it. A secondary regulator for having different pressures in different kegs is not something I would recommend unless/until you hit a point where you wish you had it - which might not ever come, to be honest.
Some store-bought kegerators I've seen come with beer lines that are way too short, leading to an unbalanced system and foaming. This is a cheap and easy fix - just get some longer tubing (10-15 feet per keg, depending on serving pressure and line I.D., etc.) and coil it up inside the kegerator.
I've also seen a lot of cheap taps on kegerators, so upgrading to all-stainless, front-sealing taps would be a nice improvement. Flow control is another nice feature, although I'm not sure it's really needed on a simple direct draw setup.
Having more than one CO2 tank adds such a crucial level of convenience that I would not even consider it optional.
While not immediately urgent, you definitely want to get a plan in place for line cleaning ASAP and not wait until your beer starts to taste like ass.