As for PS2 I share opinion with JonthanD, the best way of loading backups on a PS2 is to use HD Loader together with the PS2 network adapter and a HDD. DX has started selling clones of those not long ago if you can't get hold of a genuine one. There are versions for both PATA and SATA disks.
Personally I like to load HDL from a cd, but should be possible to install it to a memory card too. I haven't tried that myself though, so I can't say for sure if it works. Since you want to use one of the patched versions of the original HDL that are circulating on the interwebs you need a method of booting burned cd:s. Sure, swapping works, but its much more convenient to do it with a modchip. Anything goes, if you order one of those network adapters from DX you can get a modchip from there too while you're at it. They've got a really good Modbo 4 clone at $4 or something like that. If you're still not convinced about the advantages of HD loading, just order the chip :>
As for GC it's all about what features you want. I've got a XenoGC v2 in my GC. It's cheap, easy to install (just dont do the wireless install as the manual suggests, it's much easier to do it with wires, and that also makes it easier to remove the chip later should you want) , and so far it hasn't let me down when it comes to playing backups. I haven't seen anyone mention any problem games in various discussions about it either, so I assume compatibility with backups is 100%. It doesn't have all those features of the more expensive chips though.
I'll begin with explaining what a xbox chip does in simple terms. Basically it's just a storage area for a hacked bios. It also got the capability to ground a leg on the TSOP (which is what the storage area for the original bios is called) to disable it and render it invisible to the xbox during boot time. The chip then feeds the xbox the hacked bios. An alternative to using a modchip to boot the hacked bios is to simply flash it to the TSOP. To make the TSOP writable you have to short four points on the motherboard. Assuming that you want to keep your TSOP writable after you've flashed it, the rest of the process is done with software.
Modchips for xbox won't let you do anything that you can't do with a TSOP flashed box. Actually there are a few things that a TSOP flashed box can do that a chipped one can't, like running some VGA bioses, etc. The only real advantage a chip has over a TSOP flash is that it's much harder to screw up when you're doing the mod. If you manage to misflash the TSOP it can be hell to recover it, unless of course you have an xbox 1.0 or 1.1, have installed a switch to split the TSOP, and got a working bios image flashed to the other half.
In my opinion the foolproofness of a few of the later generations of modchips is their only real advantage over flashing TSOP, so I'll suggest one of those chips one I got some firsthand experience of, Smartxx LT OPX. Basically it's impossible to screw anything up once you got the modchip soldered in, before the bios is loaded, the SmartXX loads its own loader. If you manage to bork a bios flash, or maybe configure the bios to load a dashboard from a path that doesn't exist by mistake or something like that, you just reflash it from the loader. In comparison, if you bork a TSOP flash, it's not as easy to get into the flashing utility to reflash it.
Also, the SmartXX LT OPX got 2 MB of flash memory, which you can configure into banks of different sizes. Most bioses are 256 kB, some are 512 kB, so you can have several bioses installed in parallel, which can have some uses.
Then there's the softmod alternative. Current softmods are just as good as a hardmod, but there's one significant disadvantage: if you manage to screw something up on the hard disk, you might have to redo the whole softmod.
Which one of those methods you choose is just a question of preference. The functional differences are small, and all of them work equally well for the important stuff; running homebrew and loading backups both from the hard disk and burned discs.
A summary of risks, costs, difficulty levels, etc:
TSOP flashing and softmods doesn't require any additional hardware, so they're free, save for a cdr/dvdr or two. Chipping of course requires a chip :>
I recommend you to get a bigger hdd than the original 8GB one though, no matter which mod you do. Half the point with modding an xbox is to load the games from the hdd, and a 8GB disk wont hold a lot of those. Also, if softmodding, the last thing you want to do is to screw up your original disk, since it is the key to recovery if something goes wrong and you didn't get the hdd keys right or someting like that.
Chipping is probably the least risky method if you got some skill with the soldering iron. The soldering is really the only step that can go wrong with chipping.
TSOP flashing is somewhere in between, even though it's less soldering to do than if you go for a modchip, there's also the flash procedure to take into account.
When softmodding there's a lot that can go wrong, first the hotswapping of hdd:s, and then the installation procedure. If you opt to upgrade the hdd, you can always just start from the beginning if something goes wrong with the installation.
From easiest to hardest, I'd order the methods like this: chipping - TSOP flash - softmod. But then I'm far from a newbie with the soldering iron. You might have a different opinion.
Once you got the mod sorted, the modchip one is the most robust. It's as mentioned virtually impossible to screw anything up. Same goes for the TSOP flash, if you're fine with the bios you flashed when doing the mod and don't want to update it later. A softmod is very possible to bork when fiddling around with the stuff on the hard disk, if you manage to delete the wrong file by mistake, you might have to redo it. If you got your box chipped or TSOP flashed, the worst thing that can happen is that you have to install it using Slayers EvoX auto installer DVD or equivalent.
