For what it's worth coming from an APA 4/5, here's the equipment I own; anything on this list I've used at least a little and liked enough to keep. :) Items with an asterisk in the “R” column are things I specifically recommend.

Personally, I think these cues are great. The 19 oz VAL05 is the first cue I ever bought, and I just wanted something inexpensive so I could my own cue and start building consistency instead of playing with whatever random house cue I happened to get every time. Eventually I bought the Elite Heavy break cue, and when I actually tried playing with it as a joke I discovered I really liked the extra weight. So, when I bought my next cue, I got the same thing: another Action Value, but this time at 21 oz instead of 19 oz (and a different color). I like this second cue even better, although weight choice in a playing cue is ultimately personal preference. I went from being a lowly 2 all the way to a pretty dangerous 5 (and probably would have become a 6 or more one day if I hadn't stopped practicing) with these cues; I know there are more highly-engineered cues out there and maybe if you're looking to go professional (or play snooker) it matters, but if you're playing in a social league for fun then these cues will take you everywhere you need to go.

One of my pool mentors suggested the Moori medium tip back when I was first getting started; I've never really experimented with different tip types so I can't give a great opinion on how it compares, but I do know I can get strong draw/follow/spin on the ball when I hit it correctly. At $20, it's a bit of a price bump if you're trying to stay really cheap, but ultimately if you're wanting to expand your cue ball control beyond the beginner level you're going to need a nicer tip than the generic ones that come by default, and for me the Moori medium has worked well.

People like to claim the Action Elite Heavy is banned, and PoolDawg plays it up probably because it helps sell cues, but I've read the APA rule book and it says nothing about restrictions on cue weight, length, or anything else. I've also been all over the APA Web site and they provide no information whatsoever beyond the rulebook, that I can find. Therefore, the only reasonable assumption is that any cue is acceptable.

If you're willing to base your decisions on hearsay (as we all are forced to, since APA has zero official information on the subject), I've got some. As it happens, I've found anecdotal information such as page two of this PDF that seems to agree with me, but again…in the absence of any official statement whatsoever from the APA organization, the only reasonable assumption is that there are no restrictions (although the above random PDF does suggest that APA requires that you shoot with an object designed for the purpose of playing pool).

I've also heard (but again, have no proof as APA does not publish any information) that phenolic tips are banned. Assuming for the sake of argument that this is true, it might not affect you in your regular league play if your individual league doesn't care, because league rules override APA organization rules. You'd find out when you went to the national competition where the overall APA organization's rules are all that apply.

Of course, none of this is relevant if you're playing in a different league (BCA, TAP, etc.); they may very well ban heavier cues. If you like the cue but need/want it lighter, Ozone Billiards offers the same cue in weight options from 21-27 oz (presumably by removing/replacing the weight bolt).