There’s some really good advice given by @Craig6 I’ll add a little bit more
To answer a couple of your questions:
Yes the Colt LE6920 is probably the most common variant. I forget the other model numbers (6940? 6930?) but all you are changing is the different features or furniture but the core of the rifle is the same. In normal times I would say you can research a little and get whichever you prefer, but nowadays it’s get whatever you can get your hands on at a reasonable cost.
Most ARs can be customized but it’s important to know its not a blanket “change whatever you want”, some things are really easy and some are hard. If there is something specifically you want to change and aren’t sure, ask in here and get an answer rather than find out later you can’t do it.
ARs can change the furniture (grip, stock, handguard) usually pretty easily, you can add accessories (handstops, foregrips, lights, lasers, optics, sights) and change some internals like the trigger, safety, mag release, bolt catch, etc. Most often these changes require minimal tools or tools you already have around the house.
Changing caliber however (from .22LR to 5.56 or vice versa) often requires way more than that. Frequently you will need a new barrel, bolt and bolt carrier, new magwell (or an adapter), buffer & buffer spring. In some cases you might need a whole new upper receiver as well. In rare cases you need a different lower receiver too. Most people who swap calibers frequently just buy an upper in each caliber and then put it on the same lower. Eventually though those people just buying a lower for each upper. ARs breed like rabbits in that sense.
I wrote a fuzzy tier rating in another thread that may help, link below…
If you are in the market to buy “right now”, have a look at Palmetto State Armory’s (PSA) Daily Deals section. It was bone dry through most of 2020, but they seem to be getting/making more stock now. I think this link below will take you straight there, but if not from their homepage choose “Daily Deals” then filter by PSA brand.
There are a couple kits right now that are in stock at a fair price, not sure how long they’ll be in stock but . Like this one is an AR pistol kit, comes with a red dot and backup iron sights (BUIS), and 10 magazines for $900. This AR rifle kit only has BUIS, but costs a bit less out the door at $730. Both kits include a complete upper (the upper is the “hardest” to build requiring some special tools and a little more knowhow), and all the pieces to complete a lower (this can be done with tools you probably already have and watching a few youtube videos).
In both cases, these kits can be delivered to your door BUT you will need to buy a stripped lower (this is the serialized part of the firearm) and that needs to be purchased from, or delivered to, an FFL and a background check completed.