Balance certainly affects the way you play, especially when it comes to shots where you need to juice the ball or muscle the stroke. The way you bridge will be a huge factor in what balance is good for you. A forward balance weighs the cue down in front, keeping it down & steady as you stroke with a pendulum, allowing the cue's weight to swing forward & do the work. With an open bridge, the front weight keeps the shaft from lifting in the occurace of a draw shot, so the tip stays low & hits target. In other words, a forward balance is less affected by your grip hand muscles that so commonly cause a bad stroke in, but not limited to lower level players.
Your "style" of play can be summed up by how you play the game, stroke the cue & your rythm. You have fast players who shoot firm & use lots of spin, sprinting around the table like a caged animal with tense muscles. Then you have those slower guys who lightly hit the ball, letting the cue do the work & the balls never really seem to travel fast or move far. It's smooth & boring, like a poetry seminar. Everything is on que & effortless, flowing. The rest of us are somewhere between these to types of players. The first guy likely prefers a lighter cue with a neutral or slightly backward balance so he can be in control. The second guy likes a heavier cue with a forward balance, something that allows him to only guide & point the cue while it does the work for him. He doesn't grip the handle tight. The first player grips it like it's his ****. Two totally different ends of the spectrum, with a lot of players in the middle. So, are you a slow deliberate player who lets the cue freeball between your thumb & first two fingers, or are you the guy who grips the stick like a ball bat & wants total control over the movement? These are things that determine your style of play & can greatly factor in on what type of cue would work best for you. There's no right or wrong, no black & white. It's all grey. There's lots of variables & this only explains a couple basic ones. But this is what people mean when they claim a forward balance is great for their style of play.
As for shaft taper, it's a trade-off between structural integrity & comfort. A long pro-taper makes for a flexible shaft that is very comfortable to stroke, especially for the long neck strokers who stroke almost to the joint. It's harder to control spin, as it can be exagerrated & often unpredictable. A very stiff taper feels like a log, uncomfortable & rigid. It's easy to control speed & spin, but harder to aquire power spin. Quality of the wood affects this all a lot, too. Really old, heavy wood can be used in a long, skinny pro-taper & still hit stiff. Again, there's many variables. Most shafts fall in the middle somewhere. They should be a good medium of comfort & playability. Stiffer shafts produce more power, so you can hit the ball softer & still get good speed. Basically, you can finesse a shot that requires a hard hit. They also make the ball travel a little more predictable, so accuracy is easier. Flimsier tapers require you to hit a little harder for the same speed, and can be tricky as they often cause squirt that reduces accuracy. This can be noticed on long straight shots. You gotta have a good stroke to hit dead center on the cueball. A stiffer taper alleviates this to some degree because it won't induce as much spin given the same power. That means if you are on a long straight shot & your stroke is shaky, you may easily miss with a flimsy shaft do to unintended side spin. Unbintended spin will throw the ball & leave you scratching your head wondering what the f*ck just happened. The stiffer shaft will not induce as much spin, so if your stroke is a little off, you may still make the shot. It offers slightly more forgiveness in this situation. But in the end, it all comes down to personal preference, what works well for you.
My suggestion would be to find a cue that seems right, and stick to it unwavering. Just keep it & get used to it, learn it & learn to trust it. Swapping cues because this guy says this or that guy says that is a sure fire way to confuse you. You are you, and until you know your own game & play style & preferences, just stick with a nice production cue like a $250 Joss. When you understand yourself & your game a bit better, then contact a custom builder who is reputed to build cues that fit your style & preferences. From there you can fine tune, hone in on the qualities that will make a cue fit you specifically. Then keep it & don't second guess yourself, unless your game changes from the tense player to the smooth player. Then of course you might not like your old cue anymore. But by the time that happens, you'll not have any more questions to ask. I have seen world class players that don't know anything about cues, they just know how to play the game & they adjust to anything. I have seen world class players who know cues well enough to educate most cuemakers. It's all personal. You like this or you don't, or you don't care one way or the other. No big deal either way. But cues do indeed aid in how the game is played & can certainly affect how well the player performs. Some players adjust to anything, some require a perfect fit.
I hope the long winded answer helps. There's just not a simple or short way to explain it.
