Hopefully you'll have a second healer with you, your playstyle will vary if you're solo healing or not. Lucio isn't the best solo healer.
That said, if your other healer is competent, you shouldn't prioritize gold healing. In a way, you're wasting too much utility if you stay on healing most of the game.
As for when to heal or speed, you'll want to be on speed most of the time, and use heal while amping, if needed. During fights you'd rather give your teammates the speed multiplier to avoid damage and get around corners, or to chase down low health targets, rather than give them mediocre AOE healing. Don't try to switch every second like you'll see in montages. While that helps to be unpredictable and is very situational, you'll get a feel for that in time, and when it's appropriate.
Sound barrier should be used to capitalize on a pick, prevent an incoming enemy ult, or during a push to overwhelm the enemy. More than anything, you don't want to sit on your ult for too long, since you can likely build another one fairly quick.
If your team just got an elimination in a 6v6, I'd use my ult. Odds are a few of your teammates lost some health along the way, and by using your barrier you essentially "reset" them to full health for a while, pretty much guaranteeing your team the win in that fight.
Preventing incoming ults is pretty self explanatory. If you're stuck in a graviton, or see someone who might use their ult, stay aware and see whats coming. You don't want to break it down too early, since it does degrade fairly fast. The closer you use it to the start of that reaper ultimate, the better. It has a brief cast time, so ideally you want it to activate right as an ally gets into critical health. That's not always worth the chance, and isn't always possible. But again, you'll get used to it if you keep that in mind.
Similar to the first scenario, you can use your ult to push a point. You wont always be able to secure that first pick without some ultimate assistance. For example, you may be getting shut down at the first Eichenwalde choke. If you have an amp ready (and know they don't have a Mei wall ready to block you) switch to speed, break it down, and amp it up. The goal is to overwhelm the enemy with a bunch of fast, high health allies flushing past the choke to secure picks.
Amping it up should be used pretty often, but don't waste it if it's unnecessary. Out of a KotH spawn, speed amp. If you see a low health soldier trying to run away with your reaper tailing him, give him a speed amp. If your symmetra has full beam charge and is near a large group, speed amp. If the enemy is sending in any ultimate at all, speed amp to take cover. If your team is using any ultimate, speed amp. If you've just won a team fight, heal amp to top off allies. If you've got an ally on low health during a fight but taking cover, heal amp. Generally, you want to use speed to capitalize or retreat. Use it to allow allies to finalize that pick and prevent escapes. Use it to let your Rienhardt wreak havoc after a 5-man hammer down. Use it to retreat from the D.Va or McCree ultimate. If you think an enemy ult is coming soon, hold onto it and use it when necessary, being near a corner with an incoming D.Va ult and no amp is no fun. Heal amps are best used during a lull, to top off allies. Like i mentioned in the heal vs speed part, speed amp is often better to prevent the damage in the first place rather than to heal through it. But if an ally is very low on health, a heal amp is a solid choice, either during or after a fight. Amping heals makes your healing rate respectable for a brief period of time, so don't waste it. Don't focus too much on switching here either. Once you improve you can start a speed amp and switch to heal, and maintain your speed with bunnyhopping and wall skimming, but thats a lesson for another day