Usually, yes. But for just “maintaining” an AR-15, you don’t need a punch set. All you’re cleaning is essentially the upper receiver, the barrel, and bcg. You don’t need a punch set for that. Now, if you’re building one, that’s different, but a punch set is pretty the same.
You can always buy additional punch set later on, they’re fairly cheap.
What you really want to have all bases cover is a mallet/hammer with brass/polymer head and a multi-size punch set.
I bought this two year ago.
https://www.amazon.com/dp/B01M6A4ZA9/ref=cm_sw_r_cp_awdb_btf_t1_xIzoFbFBZB72B
The only part that needs to be shipped to an FFL is the lower receiver, whether stripped or already populated/built. All other parts - even complete built uppers - can just be shipped direct to door. The only part that's registered/serialized is this part.
If you're building using a complete upper (which may or may not include bolt carrier group and charging handle), you'll also need a stripped lower, a lower parts kit (which may or may not include fire control group, pistol grip and/or trigger guard) and a buffer tube assembly (tube, buffer, spring, endplate, castle nut), plus a stock.
Some places (PSA, Del-Ton, etc.) sell rifle 'kits' that literally contain everything except the stripped lower. If you can find one that has the features and price you want, that may be the way to go for your first AR.
As for tools, you can buy the ones you need to assemble a lower on Amazon:
Roll pin punches + starter punches - you'll need these to drive a couple of roll pins in (bolt catch, trigger guard).
AR-15 Armorer's wrench - you'll need this for the castle nut mostly.
This assumes you already have basic tools like a hammer, screwdrivers, some Allen wrenches, etc.
Great instructional video for building your first AR lower. This'll give you an idea of when you'll need those tools.