To be honest I don't know if messing around with multi or dual classes is the best course of action for the first playthrough. More stuff to keep track off and you will be confused enough already. Can't see it being very compelling for the first game.
It's not easy to decide what you would find most entertaining though. The "first playthrough" changes things a bit.
Usually a good advice is to play a fighter type the first time through, as they are easy to get the hang of, straightforward and effective. Play style is rather plain though as you basically just whack stuff with your sword and sometimes use abilities granted by kits. On the other hand, as a fighter you will be able to use most of the cool armors and weapons you find, and BG II has a great variety of loot, so that keeps things pretty interesting. Many weapons even come with their own abilities !
If you go that route one of the paladin kits is a good choice, as they get more resistances and abilities than plain fighters and can use the best two handed sword in the game. Alternatively, a barbarian or berserker is a good choice if you want to keep things simple. You get many proficiency points so you can experiment with different weapon types.
Another option is a swashbuckler, which is a thief kit. They get substantial bonuses to their fighting capabilities (including ability to put three points into dual wielding which makes it worth it) so they can hold their own in a fight and you get access to all thief skills. So you can fight on the frontlines and also do useful stuff like disarming traps, sneaking around, stealing, setting your own traps etc. The game is actually rather short on thieves (they are either multi or dual classed so their skills are a bit stunted) so it's pretty decent choice overall. You can fight decently but also have other options.
If you want to dabble with magic a bard is actually quite good - if you choose the Blade kit. Like swashbuckler it gives you ability to invest in dual wield which you should do, otherwise you will be stuck with 1 attack per round. Blades get access to mage spells up to 6 level. You use spells to buff up your character. You also get offensive and defensive spins which respectively significantly improve your attack or defense stats for a short while. As a bards, Blades also get to use couple of items only usable by bards. Overall, Blades get a lot of tricks up their sleeves, but require some micromanagement to keep them effective and you will need to figure out which spells are most useful. I find all that pretty entertaining myself.
If it wasn't a first playthrough I would throw in a Wild Mage. Extremely unpredictable and hilarious but probably a bit annoying for a newcomer. Sometimes you want to just cast a fireball without a cow falling on you out of the sky, your character morphing into a woman and turning yellow.
I will end this post by saying that you should probably just ignore my advice and all advice in this thread and just choose a class you personally find cool. You will probably restart the game couple of times to check out different characters anyway. Check out this guide
http://www.pocketplane.net/volothamp/bgguide.htm for tips on basic gameplay so you don't gimp yourself accidentally and you're good to go.