Hi, all, I have knitted my first project a beaded scarf (fringe is beaded). It has a diamond shaped pattern throughout, so I have learned to yarn over, knit two together, and pass over during this project. I am not sure what a second project should be for a left handed, slightly uncoordinated knitter.
That’s a pretty advanced first project. Congratulations!
I’d suggest something that requires some shaping, like a tank top or a vest. You’ll learn to increase and decrease (actually, you already know one decrease, the K2tog), and to knit armholes and necklines.
A hat would be good for learning to knit in the round.
Left-handedness really doesn’t affect what you can or can’t knit.
And as for being “slightly uncoordinated,” I’m a certified klutz and it hasn’t been a problem. Except that I get tangled in my yarn a lot.:pout:
If you knit completely left handed - empty left needle and sts on the right needle - you may have to switch the decs in a pattern. K2tog instead of ssk or sl k psso, and ssk/skp instead of k2tog. That’s probably the only problem you would run into.
I’d say a hat. You will learn knitting in the round and you can start on a small needle and then learn knitting on double points or 2 circs or magic loop. Or you can try all 3. If you want to really branch out you can even try some simple color work.
Knit what gets you excited! 
Did you decide what you are going to make next?