My goal as opener is to win before the flop, get heads up, and/or win on the C-Bet after the flop. My current understanding for sizing an opening raise before the flop is 3 to 5x the BB since less than 3x is too little mathematical pressure on the villain and more than 5x is too much mathematical pressure on the hero. But I'll be in real tournament this weekend and was wondering how to make the adjustment when the ante starts kicking in. My guess is that a pot sized bet/raise (BB+SB+antes) is the minimum needed to cause some folds.
I think your question is an important one because antes is where I definitely see the most mistakes being made in a tournament.
Your thinking is along the right lines. I'm assuming your tournament will have some sort of clock available; that clock should show you the antes and blinds. This clock is your friend, always make sure you know where you're at in the tournament and know how much is in the flop including the antes. You can pick up a lot of pots pre-flop because people will think you're overbetting, but in reality its just a pot-sized bet. Keep that number rolling through the flop too, because more players underestimate the pot at this point, and size your bets accordingly.
So, it's always (Ante x Players) + SB + BB. Thats already in the center before anyone does anything. But DO NOT just think about it as a pot-sized bet - in some early ante levels (and/or short-handed) that might not be enough to make the BB go away. So do the calculation above AND also figure out 3x BB and then decide which one makes sense to you.
Something else to keep in mind around the antes. Most players make the mistake of playing a tourney "backwards" - they are too loose in early levels and too tight in late levels. So if you use appropriate pot sizing in later levels (i.e. when the antes are in play) you're very likely to improve your stack because players will be hesitant to call those "large" bets you're making. That's where the real advantage of knowing the antes comes into play!
This depends on several factors... what's customary for the table, blind/ante sizes relative to stack sizes, who you are targeting with your raises. Early on, you can expect to get more loose calls when the blinds are low, so you'll have to raise a higher amount if you expect it to induce a fold -- maybe 3-4x if you're opening, and higher if others have already limped. Later as the blinds become bigger relative to the stacks, you'll often be able to min-raise and achieve the same effect.
Each table tends to have it's own emergent raising pattern.
In my experience the amount of the raise depends on what the table considers "normal" - like a 3x raise - and how loose the table is.
If you want to get an "effective" raise - one that will cause weak (or weaker) hands to fold - you need to find the raise amount that will get people's attention. This is always different for each table but it's usually in the range of 3x to 8x. Also, as Chris Farmer points out, when the stacks are deep, big raises look cheap as is the case early in a tournament. Also, if the table is constantly raising, a 3x raise looks like the minimum entry fee for a hand and looses its effect.
However, a big mistake many make is not making a bigger raise when there are many limpers ahead of them. You should do a 5x - 10x raise if you are raising with 5-6 limpers ahead of you - if you don't then it's mathematically correct for everyone to call - and that's a mistake. Folks who consistently "over raise" - like pushing in $25 in a $1/$2 game - fancy themselves bullies and will likely set themselves up to be felted.