Just started playing Dave's galaxy as well. Looks cool. Right now there isn't much to do other than send colony ships. I'm quite new to this though, and I might be missing a lot of things to do.
There are some upgrades for your planet, but to be honest I get confused about how much they help or hinder you. The game is changing rapidly apparently so a lot of it seems to be suck it up and find out. Right now I send out colony ships every turn. The new colonies seem to take a while to start getting useful, so I just make more and more of them. I have some automatic trader ships, which well just do their thing. Recently started making some piracy fleets to bug my larger neighbours, and a small combat fleet to try and take over some of my smaller neighbours. No combat yet but still having fun and spending less then 5 minutes a day