If you're a new comer to the serie, I would suggest going directly to the EE.
It's not THAT buggy at all, it's very stable, and a new patch (2.5) is in BETA right now.
It's really plug and play, you don't need any mod to make it run well on a modern machine.
Yes. It is THAT buggy. I can't remember the number of bugs I encountered while playing the latest BG1:EE. The worst part is, Beamdog is deleting the bug reports that are entered in their bug center. I entered 12 game breaking bugs into their system with solid proof with pictures. I did that TWICE and they deleted them TWICE. One proof that they are deleting bug reports is that there were over thousand (1000) bugs in their system 2 years ago. Now there is a lot less YET there are NON fixed bugs in the last 2 years. So a sane person should ask, what happened to those bugs?
So yes, EEs are buggy as hell. So annoying that I could finish BG1:EE in around 100 hours.
Ok, now to the original question. I finished BG1 6 times. 1 times classic, 4 times BGT, 1 times BG:EE. I could never finish BG2, either classic or EE. For BG1:
Classic BG1 has ugly graphics and use the D&D2 system which is ... not my favorite. I am not sure if mods can fix the ugly graphics or the awkward system. Of course, there are people who prefer that version. So here is a screenshot from classic BG1.
It looks like stone age to me. Also, I remember the journal was a total pain.
I Loved Baldur's Gate Trilogy (BGT). You need to own both BG1 and BG2. BGT lets you play BG1 in the better BG2 engine. The only downside I can think of is, it damages the "balance" of the game, making it slightly easier. I doubt that will be a problem for a first time player tho since the game can be quite challenging already. And here is an inventory screen from BG2.
BG1:EE provides the user with lots of nice information, both in the user interface and item descriptions. This is a real bonus, especially for newcomers. For example, now you can easily see that Full Plate Armor has +4 bonus to slashing. Moreover, the latest version (the only version I played), has some nice extra features like;
* There is a button that lets you see everything on the ground. Which makes looting a lot easier.
* You can now wield a shield on off hand while having 2hand weapons like spear or bow in the main hand which makes things a lot easier. What does that mean?
Let's say you are a fighter, proficient with the longsword and longbow. While wielding the longsword, you want to hold a shield. However, classic versions (and also 1.4 versions of EEs), wouldn't let you do that if you already had longbow in another spot. You had to take out the bow and then put the shield. In the latest version of BG:EEs, you can have them both.
Bugs are very annoying tho. Screen going crazy while taking notes on maps, quests becoming unfinishable, items disappearing from inventory, items re-appearing in inventory, gems becoming infinite in gem bag, enemies not becoming hostile which makes it impossible to kill them (even with force attack) thus you can't progress.. etc etc. That's why it took me 100 hours to finish it, most of the time spent on trying to solve the bugs. Note that I never experienced a single bug in classic versions myself.
So you can decide what version you want yourself according to the information I provided.
About BG2: I say that classic version is completely playable and looks amazing to this day. I do not see a single reason to play EEs over it. Also, if you choose to go with the BGT route, your same party will instantly start BG2 anyways, which makes things a lot easier. However, I was never able to finish classic BG2 and have not progressed much in BG2:EE so I do not think I can compare the two versions efficiently.