You say you want to get airborne quicker, but it sounds like you're having trouble dealing with enemy air in general. In this case, bear in mind there are additional things you can do to help:
- Build Missle Turrets to deter enemy air units (requires an Engineering Bay)
- Always keep marines around in case you need to swat some flies
- If your economy supports it, a few Thors from your Factory can also help.
I think it's important to know how to deal with enemy air even if you don't have a large air force yourself. This way, you can handle surprise void rays or mutalisks even if you are not pursuing an air-based strategy in a given match.
Another reason to consider learning how to counter air from the ground is that Terran air units can require some finesse. Terran air units aren't like marines, who can do anything; each has a specialty and can be very vulnerable outside that niche. Specifically:
- Vikings are primarily an air-superiority fighter. Their ground mode is weaker and vulnerable.
- Banshees are a fantastic base attacker, but can't hit aircraft.
- Ravens have great abilities, but no attack. They require lots of attention.
- Battlecruisers are powerhouses, but are very expensive and require some support.
So, to answer the original question, how to get airborne, I would say try experimenting with Starports after your Factory, and building some Vikings. Use them for base defense and as an air escort for your marines and tanks, but don't try to use them as a primary attack force until you learn their strengths and weaknesses. And don't forget to invest in marines and missle turrets.