I'm not gonna nit pick anything, so go used and cheap if you like except for the mask and fins.
I suggest a pair of jet style fins (Jet fins, slipstreams, those new hog ones, whatever) with spring straps. a good setup will be around $100 (new) but its worth it and they hold their value. Tech divers love them so if you decide you don't like them you can sell them for almost what you paid. That can't be said for the split fins or cheapo fins.
Also a mask is generally something you need to try on to get right. Thats not always true but most will agree I would think. However Dive Rite makes a mask that is guaranteed to fit/seal and I got mine online and its the best mask I have ever used. That wasn't a cheap mask at about $50 (new) but it's worth it IMHO.
If you live in warm water gloves wont be required but most times a hood is. You might look into one.
A cheap J-tube snorkel or the more expensive fold up snorkels are gonna be your best option. I have NEVER needed or carried a snorkel past my open water class.
Do you have a budget? PM me and I can shoot you some good sources to check out for gear. T