Hand down, the DMS4 Pro E.Z.I. I've had it for years and it's the BEST chip yet. It's super easy to install (no soldering needed) you just pop it onto the chips and it's done. Best thing about it, is that it has a flash part to the chip so you can install "Toxic OS". Toxic OS will allow you to boot from either a HDD or DVD/CD. It will also boot from a Memory card (Homebrew) or allow you to install Homebrew and games to a HDD.
The only downside is the price, it'll run you around $80-100 for it. (I'm sure you can find it for lower if you shop around) but still if you play your PS2 a lot or plan on it, it's the way to go.
If can't afford something the chip, then I'd go for the Memory Card Exploit and PS2 Menu. The MC Exploit is rather simple to do, and works on all (I think) versions of Ps2. You need a original PsOne Disc and a Memory Card with the exploit. What the Exploit does is allow you to boot homebrew from your Memory Card by use of a PS One Exploit. It's fairly simple to do, and if you load up the MC with PS2 Menu (A Gui of sorts to launch different Homebrew) you can boot into HD Advance or a CD/DVD Swap program. The downsides are that you need someone with a Modded PS2 install the Exploit on your Memory card for you (since usually you've got to boot a burned disc), and do to do the swap you'll need either a flip top top (which can be modded yourself or bought, or even if you do what I did just take the whole lid off of your PS2). Also, to do the swap you'll need a original PS2 DVD game that's about the same size of what you're going to play. I've always used the Devil May Cry demo since it had the largest Table of Contents for a DVD5 game.
So in conclusion:
Best bet:
DMS 4 E.Z.I PRO
+ Easy Install
+ Boots from CD/DVD/HD/MC
+ Has a "O.S."
- Price, near $100 OUCH!
Not so bad:
Memory Card Exploit
+ Free
+ Allows the booting of HD Advance and other CD/DVD Swap programs
- Need to get the Exploit ON the MC by use of A) A modded PS2 or B) Memory Card device (not sure if that works though)
- Not all games work via swap (99% of them do though)
- Need a flip top lid to do the swap tick
- Need an Original Ps2 Game to do the Swap trip (TOC can be the same size or larger)
Swap Magic is also a good investment if you want to spend some money. It basically takes out the need for an original PS2 game, and the Memory Card Exploit.
Hope this helps!
I did the MC exploit for YEARS before I got a DMS 4 and I LOVE my DMS 4.