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First, I'd advise not going mad multi-tabling. If you're just starting, 2 tables is probably enough. Any more and you risk not being able to properly pay attention. The first priority is to improve so if you think you can do that on 4 tables good for you, however I think you should try different numbers of tables from 1 to 4 and evaluate where you are best able to pay full attention to your play without feeling rushed.
Beware of being oriented towards results, when you say you've made some money, I don't want to be discouraging and it's good that you have, but you need to bear in mind that in poker you can play correctly and lose money, or play badly and win money in the short term, since it's not just skill but also luck. Over time, the luck evens out and the skill takes over, but the long run is _very_ long - until you have 20,000 hands you can't even really begin to draw any conclusions from your results, and to trust that any conclusions you do draw are reasonably accurate you probably need 50,000 hands.
If you start feeling good when you win and bad when you lose, you'll never improve, since you are using the wrong source of feedback for information about how you played. You must base your feelings about how you played on the quality of your own play and not the results. Of course, at first, you have little idea how to evaluate the quality of your own play, but you must try to develop this ability since otherwise you'll never know when you're doing the right thing or the wrong thing - the results you get will _not_ tell you.
For opening hands, a lot of people will tell you that you shouldn't use a fixed set of hands, but when you're just starting I think it's useful since you can't adapt yet since you have no base to adapt from. This: http://www.gamblingsystem.biz/books/2p2NL6max.pdf will probably be quite helpful, and if you look in the archives and sticky threads here in the Beginners Circle forum you'll doubtless find other similar guides.
Starting hand selection, when you are just starting and have no real handle on post-flop play yet, should be really really tight. You don't want to play "speculative" (marginal) hands, that require good post-flop play, since although you may be able to make some money from them later once you know how to play them postflop, right now you want to be playing hands that have good potential right away and don't need 2 or even 3 streets of postflop play to return a profit.
If you're playing full ring, you want to be even tighter than if playing 6max. At first, pick one and play only that, since it will help you develop a base from which to work without trying to learn too many different things at once.
For 6max, here is an OK (but doubtless very improvable) suggestion for hands you can open:
UTG: {66-AA,AK,AQ,AJ,KQ}
UTG+1: {22-AA, AK,AQ,AJ,KQ,JQ,KJ}
CO: {22-AA, AK,AQ,AJ,KQ,JQ,KJ,AT,JT,AXs}
BTN: As for cutoff, but if the blinds fold a lot when you raise, so you immediately earn the blinds, then you can add a lot of other hands like KXs, any ace, suited connectors like 89s/78s/67s etc.
I am sure that this can be seriously improved upon, but I suggest that you stick broadly to it since the first priority is to play tight. You can loosen up a bit later and play more hands once you have a bit of experience.
When you open, raise to 3bb. If you have AA/KK/QQ/AK and it's opened already in front of you for between 2 and 6bb, raise to 3 or 4 times whatever the original raise made it. For example, if you have QQ on the CO and the player UTG makes it 3bb, raise to between 9 and 12bb. If it's raised AND reraised in front of you, fold everything but AA/KK and either reraise to 2.5x the reraise (about 30bb in our example above) or just shove all-in. These are really coarse starting guidelines, but they're better than nothing.
You should almost always be opening for a raise, and rarely or never calling. When you open, you have the initiative and can take the pot down with a bluff later much more often than if you were passively calling preflop.
Hands it is OK to call a raise with with are the smaller pairs (say 22-99) so you can setmine - if you have 33, cold call with it and hit a 3 on the flop for a set, then you can start raising postflop, otherwise you are folding to any bets on the flop.
NEVER limp (limp means just call the big blind). You can call a raise with the smaller pairs, but if it's not already raised in front of you, raise with them.
Other than that, at first I would not cold-call at all. Raise or fold. With TT+ re-raise preflop.
Be aware of the absolute, overwhelming importance of position. It is more important to be in position (closest to the button and hence last to act on every post-flop street) than it is to have good cards. Position is everything.
It's good that you seem concerned about wasting hard earned money - do you have any idea yet about bankroll management? Because of variance (luck) you need at least 40 buyins at the level you are playing, so if you're playing 2NL ($0.01/$0.02) with a $2 max buyin you need at least $80 bankroll, I'd advise more - I use 100 buyins but some would say that is excessively risk averse. Lots of good players have busted out playing games too big for their bankroll, you must have a BIG buffer to deal with a bad run of luck.
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