No homebrew, in my opinion you are missing out but it is your machine.
As for "changing" short answer, no the USB stick is just a substitute for the memory card. Once you have a modded xbox you can probably get rid of the AR as your modded xbox is just as capable or transferring the files.
AR disc? Most AR stuff I ever saw was a piece of software to interface with the USB and FATx of the memory card*.
As was mentioned only a select group of memory sticks will work with the xbox, more on this here:
http://www.xbox-linux.org/wiki/Xbox_USB_Compatibility_List but long story short yes you can skip the AR part if you do not have card but a working USB stick.
Link of interest:
http://www.xbox-linux.org/wiki/Getting_Started#26_27
*one thing I will mention is insert your USB sticks after booting and the softmod has loaded up or at least select read only mode, the xbox will autoformat it to the FATx if not.
Back on topic softmods can boot commercial games and I can give you a bit more advice on the subject.
2 methods for running games on the xbox.
Off the drive. The stock drive is 8 gigs but the later models are 10 formatted as 8, this will give you around 5 gigs to play with if you extend the partitions. Most games are around 2 gigs but that can go either way. Many scene releases are ripped to fit on a single layer DVD, more here:
http://www.abgx.net/filename/
Replacing an xbox drive (IDE is up to 500 gigs these days) is fairly simple, two main methods use a tweak on the hotswap softmodding method and the other is done via telnet and the xbox itself. Naturally you have to open the thing up to do it.
The only problem is for a softmod you need a drive that locks. Locking is a rarely used part of the IDE spec and as such some do not do it and can not be used in a softmodded xbox, this would be the other reason for using a chip which can bypass this whole mess but not a very good one if you only do it once.
List of drives and data upon them when it comes to the xbox:
http://xboxdrives.x-pec.com/?p=list
One guide of many:
http://forums.xbox-scene.com/index.php?showtopic=244043
Some pay attention to rotation speed (5400rpm was standard for much of the original run of the xbox and so that list whereas now it is 7200rpm or more) and the fact the drive gets pretty hot, in my opinion it is overrated but worth paying attention to at some point.
Bonus is that you can have trainers and there are lot of good ones available.
Off of a disc.
I seemed to forget to mention the lousy drive the xbox ships with (later models are better but far from ideal) so here is the link I would have given had it not been 2:30am (irony noted):
http://www.xbox-linux.org/wiki/Xbox_Linux_...D_Burning_HOWTO
You can change the drive for a shiny PC drive though (which if you need a read only one sell for hardly anything these days and will do it all:
http://www.xbox-scene.com/articles/dvddrive.php )
None the less you can burn an ISO and play it all dashboards worth anything forget region coding exists.
2.4 gigs (or less) is a waste when you have 4.35 to play with so you can make multi iso discs, usual method is to burn it with a dashboard on the disc which allows you to select your game but you can just burn a bunch of games and launch from a file browser on a normal dashboard (not a method I suggest doing, least of all if others less technically inclined are to use it at some stage).
Several tools are available, I like C-xbox tool myself (comes as part of Xbox HQ PC essentials which comes with AID) which acts as a frontend to menux and MXM. It also has some mean iso manipulation abilities if hacking is your thing.
Caveat: iso standards tend to mean alphabetical order of files whereas common sense dictates keep common files close to each other. Star Wars knights of the old republic was stickler for this (loading pauses where there were none). Read more here:
http://forums.xbox-scene.com/index.php?showtopic=226194
Note the newer dumps are 1:1 and so not affected by this and most games could not care less.
Hard drives and to a lesser extent swapped/replace disc drives are not affected owing to higher read speeds.