Leave them alone until you get better ships, higher level caps.

Or, go Advent and pound that Shield Regeneration button repeatedly.

Your light frigates have a nasty habit of targeting the flak frigates first. This is a bad idea(tm), as flak frigates are mostly harmless to your ships, and have FAR more health than the other ships. Tell your frigates to bust the other, more dangerous ships first. Kodiaks, LRMs, and light frigates will end up killing your ships if you leave them be.

I normally go two capital ships right off the bat and I've found that two capital ships are more than a match for even a Terran planets militia if you use them right. If all you do is kill the siege ships like CMK mentioned above you could even move on to the next planet and the next just doing that until you've got a lot of planets.

You can avoid this problem by getting a battleship cap instead of the colonizer. As advent, there hasn't been a single planet I couldn't take with a radiance, though sometimes your ship will get hurt pretty badly.

I agree with one of the other replies. Sometimes, your ships will target the flaks or the cobalts first, which is not necessarily the best of ideas. If you have a carrier cap, then yes, target the flaks, but if not, go for the harder hitting units first, like the LRM's. Think: Kodiak - priority, then LRM, cobalt, siege/garda. That generally minimizes the damage taken to your ships by eliminating the most powerful ships first/the most deadly to your starting fleet. If you come across a neutral colony, its generally best to avoid it if it is larger then normal, until you have a larger, more diverse fleet at your disposal.

its easy to take out the militia's of most terran/desert planets with a modest fleet.

you're usually up against something like this:

4x Cobalt Light Frigates
2x Garza Flak Frigates
2x Javelis LRM Frigates
3x Krosov Siege Frigates
2x Kodiak Heavy Cruisers

that's a typical militia. you'll notice that the kodiaks and javelis are the only real damage dealers in that bunch. focus fire on those first (javelis first then kodiaks) and you'll take much less losses. take out the cobalts next, then the garzas and finally the krosovs.

this kind of militia is pretty easy to take out with a fleet of as little of 1 Capital Ship (leveled up to level 3) and 6 frigates (some mix of light frigates and LRM frigates, i like to use 2 lights/4 lrms). you'll probably lose 2 or even 3 of your frigates but you'll take out the militia no problem and gain alot of experience for your cap ship, which is worth alot more than 2 frigates anyway.

I personally don't even bother with cobalts/frigates. I just upgrade to LRM's/Assaliants and make about 6 of those with a battleship(not colonizer). Send in your cappy first, than your LRM's. If the kodiaks start to focus on the LRM's(probably will), hold, but when the lrm is about to die, send him back to your closest colony. Than when the next lrm is about to die, repeat.

I save a lot of money by just using two capital ships. I've gone to get 5 or 6 planets in my empire with full trade depots ect with just 2 capital ships and nothing else. If you use them right the only thing that can stop you is a pirate planet or the enemy fleet. All the while I've not upgraded my fleet at all so I'm getting full income from my planets with no fleet over head. It's worked very well for me so far.

Hmm, didn't realize it was a problem. It's not for the Vasari. Just Build a Jarrasul, and take what I want. Can go through pretty much any militia, colonise a planet, and move on to the next planet, usually without waiting to heal. It's only a danger if there are 2 or more Kodiaks, two I can usually go through still, but it'll leave a single Jarrasul all banged up. I research Regeneration Bays as fast as possible, and put them in pretty much every system, and just make two trips to the nastiest planest.

However the other races can build two caps sooner than the Vasari's so it should work out.