One high priority early on is to expand your military academy so that you can acquire a decent selection of civilian admins and scientists as quickly as possible. A scientist with a 25% bonus will double research speeds in his specialty and an admin with a 20% bonus to factory production will greatly speed up economic expansion.
Another high priority item is the research and construction of the sector command building as that'll provide a fairly substantial boost to production across the board (If I'm recalling correctly, the sector commander provides 30% of their bonuses to every body in the sector).
Other than that, it really depends on your mineral setup. One thing you can do to help in that area is to avoid doing a geosurvey of Earth until you can commission a team with a decent starting skill level (At *least* 120).
Don't worry about producing much infrastructure for colonies as your population produces a significant amount on their own as a trade good. You mainly just need a small amount that you can manually place to trigger your civilians to start transporting it.
The mine/automine question depends heavily upon the success (or lack thereof) of your geosurvey ships. If a planet like Mars has a substantial amount of minerals (with fairly good accessibility), you may be able to get away with producing a substantially smaller number of automines than if you were in the situation that I found myself in in my current game: Mars and Mercury had nothing, Titan had a substantial amount of duranium with modest accessibility but not much else, and I ended up having an incredibly lucky geosurvey team on Venus that turned it into a pretty decent mining colony overall. Still, I ended up with fairly substantial (100 or so at peak) number of automines on asteroids simply because Venus, despite being the best of the smegty options I had, didn't provide me with the quantity of certain resources that I was in desperate need of (Corundium being the biggest).
Building a PDC on your capital is a fairly low priority, so don't worry about that early on. One option once you do, though, is to add a fairly large number of hangers so that you can "mothball" military ships, so to speak, and avoid paying their upkeep. As to how effective that ultimately is, I cannot say for certain, but it's one possibility. However, once you start colonizing, be sure to start construction of a prefab PDC early on (5mil might be a decent point to start) if you'll need the protection rating as it will go incredibly slowly with a single CF.
Orfeusz makes an excellent point re:economy when it comes to overbuilding construction factories and research labs, but should you find yourself with economic room to spare, I'd put those two at a fairly high priority. CF expansion depends heavily on your current and near future mineral production, though. If you find yourself spamming a massive number of financial centers due to a duranium shortage, more CFs probably isn't a terribly wise investment.
I'll disagree with orfeusz re:mass drivers, though. If you're dealing with a mineral shortage, their ability to provide near immediate access to mined resources could be a life saver. Not only would you be better off using your first generation freighters to periodically collect the minerals and use the 300BP per driver for something else when you're not dealing with a shortage, but provided that you're actively expanding the mining colony, your freighter will likely be visiting frequently enough so as to eliminate the need for a mass driver even during shortages.
One advantage of mineral shortages, though, is that it's pretty easy to determine what to build. For the longest time I had a duranium, mercassium, and corundium shortage, so my CF designation was pretty straight forward: Just enough auto/mine and research construction to maintain a stable resource level with the scraps going to whatever pet project I had at the time if I had spare duranium or more financial centers if not.