Hold just the essentials.
Nippers, tippit, floatant, and some flies.
Here's an old school bag for those interested;
And lanyards that carry a little extra.
I might use more filson if it wasn't so bloody heavy.
What is it you feel you're lacking? Line control? Presentation? Reading water? A lot of this is time on water, so you have to get out there.
Is there a stocking program near you? Those fish are usually easily caught and will give you a lot of experience with the hook set and landing fish.
Check out the club as they may have beginner fish outs.
Join an online forum and look for guys near you that may offer to take you out.
Ask at the local fly shop - a lot of them organize trips for novices.
Lawn casting is fine, but as CW says has zero to do with casting on water. Every piece of water is different than the last and requires a unique approach. When you approach a new piece of water you have to take the time to A) figure out where the fish are; and B) decide how best to get to them.
If you do want to practice on grass take an old leader and tie a loop at the end. Put a screwdriver through the loop and push the screwdriver into the ground. Pull out 30' or so and step back until there a slight tension on the line and practice roll casting. The tension replicates a water load on the line.
Some nice old reels.
Grass casting is worth it only if you can't get to water.
I learned the basics on casting ponds and was reasonably okay. Then I got to a river and found myself faced with 20 different casting problems that made all my practice pretty much useless. The easiest cast is a downriver load and a plop upriver. Mend once and you should get a good enough drift to fool a fish. That cast (mastered across both sides of the body) is used more than any other.