I've been interested in trying the franchise for some time now, but I do not own a PSP,3DS or Wii.   It happens that I still have my old PS2 working just fine (Fourteen years old console) and there are two MH games available for it.

Does anybody recommend ?  Are these game worth looking for them ? 

From what I know (could be wrong) the PS2/PSP versions are similar (dunno if PS2 version was better, only have PSP version). The games themselves are pretty fun but also frustrating if you suck at it like me. There's a lot of early gathering missions and prepping before you even start hunting missions. You also need to figure out which weapon type you'll use (that'll be a super important decision in some missions). There's a ton I dont understand (Im a MH n00b) but its definitely a great series if youre willing to completely learn it and are willing to put a decent amount of time into.

There's only one localized Monster Hunter game on the PS2 and it's the first one ...

I personally think it's an awful series ...

I hate this series so much to the point where looking at the game cover gives me a headache ...

I think the games benefit from online and PS2 didnt have great online back in the day.

There is no way the PS2 version's online server is still running :). The series has evolved a lot since the initial version, in terms of making things a bit less tedious (I've read that in the original, item storage could only hold ~10 copies of an item in each slot instead of 99). Maybe you can find yourself a cheap used PSP on eBay and pick up the classic MHFU (or MHP3 which is only released in Japanese, but the PSP isn't region-locked).

The games WERE amazing at the time they released.MH games are mostly multiplayer, once the online server shuts down, there's no point in playing anymore.The single player it's only good if you use cheat codes and play it like 30 hours at most, and this is coming from a guy who LOVES MH.The best thing you could do now if you want to experience the franchise, is to get the latest game which is MH4U.

Edit:also the MH Wiki is a great place to familiarize with the MH universe.

Buy it on ps2 these handhelds and the wii arent that much stronger than the ps2. just get propper component cables

It doesn't matter how powerful the PS2 is, it just doesn't have a good selection of MH titles.  However I think MH1, MH2, MHTri servers are all shut down, so the only non-hacking options for online co-op would be the newest MH4U (or else a Wii U with MH3U)... Or Monster Hunter Frontier, I guess.