According to PCSX2's compatibility list, all the PS2 games are playable, though that in and of itself doesn't say how hard the are to run, or errors that might happen/workarounds to bypass them. You may want to check the PCSX2 wiki for specifics, though you may/may not risk potential spoilers if such. I've been playing them via loader on my PS2, with them installed on a drive. Infection and Mutation worked with OPL 0.9.1 with some voicing issues (only the actual CG cutscene voicing would play, leaving combat sound effect only and most non CG cutscenes with muted characters), but Outbreak I couldn't progress in due to freezing. Switching to OPL 0.9.3, the game plays just fine, and even the rest o the voicing is functional. As a side note, I tried using HDL initially and the game would always crash just trying to load The World, thus I couldn't actually play with it beyond the ALTIMIT interface (emails, news blotter, etc)
Anyhow, the games are indeed interesting (at least up to where I am in the series; aiming to play G.U. after I finish IMOQ), and playing them digitally via emulation or loader will save you a bunch of money on experiencing them. Plus, playing them after the fact of their release means you weren't subject to three months of blue balls between each individual entry (IMOQ is basically one game split into four releases: Infection, Mutation, Outbreak, and Quarantine). However, it should be noted that the games are repetitive (they're basically single player MMOs; that's not an insult either, that is EXACTLY what they are meant to be), The World itself is rather boring (IE: the actual MMO being simulated; what is interesting is how the game continues to deteriorate and affect the real world, and Kite and co's not-so-legal efforts to fix things), and for an action JRPG you sure do spend a lot of time in the menu due to not having the option to map skills to the controller (I hear that got remedied with the games after IMOQ). The pacing also has some issues: Being one game split into four, you naturally don't find all the bosses or experience all the content in a single game, but Data Bugs aside (think glitched normal enemies that under ordinary circumstances could not be bested without Data Drain to absorb the corrupted data and forcibly overwrite it), Infection itself only has ONE main story boss (two altogether, counting the bonus dungeon boss. Mutation on gets a bit better as to boss fights (and thankfully none thus far in my experiences have been as broken as the one in Infection, but he has actual meta reasoning to be so ridiculously strong), but it's still about three per game by my estimates, one of which being a recurring boss I've fought in both Mutation and Outbreak thus far, and expect to fight yet again in Quarantine. Quarantine itself might have the most bosses in the series; by my calculations from the game lore's "Epitaph of Twilight", I'm probably going to have at least four bosses there, maybe more.
Another thing to keep in mind with .hack is that as a series it is heavily multimedia, and was intended as such from the start. Probably one of the few successful attempts at such. However, this means that while Infection is the first game in the series, it is not the first work chronologically, and the universe tended to build on itself. That said, as far as predecessors go, .hack//Sign (an anime) seems to have the most relation to the first set of games, being a prequel. The games don't necessarily expect you to watch Sign first (though cameos of prior characters and callbacks to the events in the past do have more meaning and foreshadowing if you watch it), but the anime sure as FUCK expects you to get invested in the games after it. It's also a bit of a strange show: For an anime based on an MMO setting, there's not very much actual combat. Instead, the writer actually understood that a lot of time in MMOs is just spent in character-to-character interaction, resulting in a series that is very dialogue and character driven, but without a huge amount of action until it starts wrapping up. It's not for everyone, but I do feel I gained a good bit in watching it first before playing the games set after it. Also has a really damn good soundtrack regardless of what you think of the rest of the show (an OST which Victor Entertainment does their best to prevent those living in the US from listening to on jewtube). Here's a sample.