Usually TOP players know "that timing stuff" that will never work for 'beginning' players. I've passed my way from gold to plat and see (from own games and replays) that too often low level players don't build SCVs constantly, are supply-blocked often, don't spend all mineral/gas, etc... Though you need to manage to get those PRO players timing things, it is usually too hard to do.
My recommendations are based not on exact timing "when to push" (you actually don't need that), but more concentrated on IDEA how to determine what is a good time to push.
And as always, answer depends on your opponent race significantly.
Idea is based on the empirical observations: in 90% Zerg is doing FE (either 15-hatch, or 13-pool, and then 13-14 hatch).
on 2 players map - immediately after beginning to build 1st rax send 1 SCV to scout opponent.
on 4 players map - scout right after beginning to build supply, send 1 more SCV after beginning building 1st rax if you didn't find opponent base.
The purpose of those items to build bunker on opponents natural (also is good to get 2-3 more SCVs to build 1-2 more bunkers and repair them, also 2-3 rax are required to keep pressure on). If he is going for FE - you will put a solid pressure and delay/deny his expansion, or at least will force him to build a lot of zerlings except of drones. Use this time to make own expansion.
If he is going for 1base-roach (you will see that on absence of FE - and MUST to scout what is going on) - switch yourself to marauder build and don't over-invest in bunkers (they very useful to defend against zerlings, but don't give you too much against roaches).
So From my perspective "Early pressure strategy" (Bunker rush?) is more powerful, therefore answer is: do push as early as possible at least on plat-diamond (and probably master) level. I not sure how will that works on bronze level. Problem is not in opponent, but in your micro: you should be able to manage to survive your 1st SCV, in parallel you need to build more SCVs, more barracks, more supply depots, probably expand.
Idea is based on the empirical observations: in 90% Protoss is doing gate+core+1zeal+1stalker+2-3 more gates.
Again, from my experience against plat-diamond players, your should push ONLY when you have concussive shell and 2-3 marauders. Till that time you also should have 2-3 marines (while you building refinery and spending "early" gas on upgrade/marauders you should have some possibilities to build 2-3 marines).
Would be good to start stim-pack research earlier then concussive shell. In this case using kiteing (shoot-and-go) you will deny harassment of you army if you decide to turn back. Also you should be able to deal with first zealots/stalkers easily.
Taking to account 3-rax plan, usually you should have 2 tech lab and 1 reactor. But I would suggest to deffer reactor a little bit. build "in parallel" 2 tech-labs, then 2 marauders, then start 2 upgrades. Once your marauders ready - take your marines, go and push with them.
So answer is: as soon as you get 2 marauders
Cant say you too much, that is VERY dependable what your opponent is doing (again, I'm talking about plat-diamond players, but if you planning to improve your skills - try to do your best).
There are 2 most common Terran strategies:
- 2 rax FE (or as variation) marines push;
- 1-1-1 build (or as simplification 1-1 build as we will see the very beginning - when player didn't build starport yet, or just didn't build any units from that; but player does build tech-lab on factory and is researching siege mode).
Case when your opponent start from 1-1 build and siege mode research. From my perspective, your marine push will fail here. If you start "Very early" with 7-8 marines, and opponent has 3-4 marines - he will just take 5-7 SCVs and will be able to survive long enough to get 1st tank. After that you push will fail.
If you wait for 12-16 rines opponent will have 1-2 tanks in siege mode (with some rines too) and you will fail also. Though, it depends from both of you microing skills... there are options to manage to kill those tanks and keep pressure with stimmed marines.
But for sure that will fail once you go to higher league, so I wouldn't recommend to invest to much in this strategy.
Therefore for case when your opponent start from 1-1 build - try to invest in expansion. Though take into account: soon he either bring sieged tanks to your door, or will make marine OR helion OR tank drops, or Banshee harass.
Case when your opponent start with 2rax FE. Scout him (scan?) and if you see he is building CC - put pressure right now: he has exactly same amount of marines as you -8. If you manage to deny his expansion without loosing more then X+8 marines (X - is amount of marines you kill from opponent) - that's would be good. Otherwise - you will fail.
Case when you opponent start with mass rines and stim research: doesn't matter when you push - you will fail as he will have more reinforcements. Again, it depends from your micro skills, but if you see he is going to mass rines - think about few bunkers and expansion.