To answer your questions it is probably easier just to explain what 360 modding is. Getting to it there are three main categories of mod for the 360, do note any mods can see you banned if you do not play it properly. I will probably be a bit link light today.
1) DVD drive flashing- most people that hack a 360 will do this as it allows all disc based games (give or take this recent AP25 stuff) to be run. A lot of DLC comes on discs in various forms in game of the year editions so you do have some options here as well.
Anybody can mod a DVD drive and unless MS pull another AP25 on us there is nothing a dashboard update can do to trouble DVD hacking- those that do it can effectively treat their 360 as a normal 360 that also runs copied games.
I lack the space and time to cover DVD hacking in full right here but generally it involves dumping the keys (usually the trickiest part and one MS tend to make trickier as time goes on), using the keys to build a new hacked firmware and flashing it back. Everything else is just methods for each part (the jungleflasher site has a nice guide to it and is the main program people use for DVD hacking related stuff).
2) JTAG/SMC hacking (previously the king kong exploit)- been around for a while in various forms but in August 2009 MS blocked the current version in software and prior to that in June 2009 they blocked it coming out of repair shops and the factories.
This does not allow copied DVDs right away (you can dump DVD keys with it though) but it does allow easy use of XBLA, DLC and hacked games/trainers among a lot of other niceties (controller remapping, region free, system link over the internet as long as the client box is patched to allow it- host can be stock, USB loading, hard drive loading, having any SATA drive as a 360 hard drive and homebrew to name but a few things). MS block this by triggering/blowing fuses inside the CPU so you can not downgrade to earlier firmwares and use the exploits that it requires- this is why this sort of thing will not trouble you. Freeboot (and older methods like XBR) allow JTAG users to use the latest dashboards and thus play the latest games/have all the nice features from the latest dashboards- this is what this thread is about.
3) Hard drive hacking (now also USB hacking seen as MS allowed them in a fairly recent update), programs are many but mainly USB wants XTAF and hard drives want xplorer360,
http://360.kingla.com/ is also worth having if you play around with this for long enough. There are various exploits, tricks and techniques that can be done- a while back there was a bug in modern warfare 2 that allowed some XBLA demos to run as full.
There is profile sharing (requires live) and has undergone something of a resurgence of late that allows DLC and XBLA to run (although I do not like it) and there is profile hacking (mainly to add achievements points without earning them- MS ban people hard for that though so do not bother with it). Do note profile sharing XBLA and DLC is different to scene release XBLA and DLC which is aimed at JTAG machines.
Similarly an older version (you will have to find it like you would a rom- the one from XBL is patched and nothing you can do about that) of shadow complex (often considered one of the best XBLA games) that you could glitch into allowing you access to the full game (there was a "end of demo wall" you could get over).
Some of the DLC mentioned in disc hacking above can be parachuted onto the hard drive along with title updates (which you can control to allow access to certain bugs in single player*) and work. I posted a list in another thread a while back but stuff like the first two borderlands DLC, fallout 3 DLC, many GOTY type games and a bunch more so it is worth looking at it.
* XBL always wants the latest title update.
On top of this there is a measure of map hacking (straight up hacking with stuff like live2con and Halo has some stuff to allow you to custom build game modes on PC rather than fiddling with the controller for a half hour) and more commonly save hacking (there are many editors for many games).
Similarly you can make your own hard drive as there are some models you can dupe the 360 into believing are official drives, see hddhackr for that.
Other stuff/conclusion
There are various methods that take a bit from each camp and do nice things with it- sec data restoration (helpful for banned consoles) takes from the JTAG camp, region swapping which can not be done without the CPU key in which case you would probably have a JTAG machine takes from the JTAG camp, it is not really a hack but XBLA demos can be added to burned DVDs (even stock drives), the AP25 stuff can be counteracted by JTAG, JTAG owners tend to spend a lot of time messing around with the hard drive (not to mention they can use FTP to manipulate drives where others are limited to USB or hardware) and hard drive hacking adds niceties for all fields of hacking.
Anyone (aside from the slims which are waiting on a DVD hack- AP25 delayed it) can do 1) and 3) but as long as you can live without xbox live then JTAG is the ultimate 360 mod at this point in time. Seen as no new ones have been available for about a year and a half now (and as it took a while for the later models to have the hacks ported/made available they are even less common) and they are that nice to have you can expect to pay a premium when picking one up (indeed if you find a pre August 11th 2009 model or one made before mid June 2009 then pick it up as you can sell it on at said premium).
