If fighting is sure to result in victory, then you must fight! Sun Tzu said that, and I'd say he knows a little more about fighting than you do, pal, because he invented it, and then he perfected it so that no living man could best him in the ring of honour.

Learning the basics of rocket jumping will be incredibly helpful and enable you to move around the map/get into favorable positions much faster.

Soldier, like demoman, also has a lot of area denial capability that lots of players don't take advantage of. If you're aware of an enemy team around a corner, try to get splash damage on that position to make the enemy team softer when they eventually push for your teammates. You have plenty of ammo- use it!

Combining this with rocket jumping, learn what sections of the map you can get advantageous angles on blenemies by rocket jumping. Lots of buildings in TF2 don't have invisible walls above them, so rocket jumps can get you angles up above the buildings to take distant shots at engineer nests.

On engineer nests, don't just pelt the sentry in a 1:1 scenario with the engineer healing if he has a dispenser behind it. Try to get splash damage on the dispenser and the engineer before the sentry (this changes if you have team support). The direct hit is an amazing weapon at taking out sentries so make a loadout with it.

Personal thing, but I find the original much easier to use than the stock launcher when it comes to placing shots, so give it a chance if you haven't and see which ones feels better to you.

If you have specific questions feel free to ask and I'm glad to weigh in.

Get the boots that reduce rocket jump damage and then rocket jump everywhere to get a feel for it. Then take the boots off and rocket jump everywhere until you learn to do it without killing yourself.

All rockets require various degrees of shooting where the enemy will be, rather than where they are, but it also helps to shoot where they might be - drop a rocket just past a corner or through a doorway just in case someone's approaching from the other side. Worst case scenario you can be confident nobody's right on the other side.

You can surprise people around corners with rockets, but if they can see you firing they're probably gonna dodge it past medium range. Get closer so they cant.

Just like you can rocket jump off the blasts, you can knock people around with them. Throw them at the walls behind snipers to knock them off their perches. Knock the scout into the chasm. Separate the medic and heavy.

If you don't have reservations against dying early and often, I'd say spam rockets at enemies (mid-range and closer) to get a feel for the rocket's trajectory/speed. You'll learn how to lead them better.

Additionally, aim closer to enemies' feet. You're more likely to hit them, and if you miss they'll still be hurt by blast damage. More importantly, hitting their feet directly slows their momentum for a quick bump straight upwards. You can either follow up with another rocket or a few shotgun blasts (get used to Q for switching!).

Lastly, prioritize Nazis and other fash. They don't get to enjoy things.