Vasari in general are best for mobility....try them out, they are fun...phase stabilizers allow you to jump between any of your planets in one jump, and kosturas allow you to jump to any enemy planet in one jump....lots and lots of fun...
General counter system:
Light Frigates, or LFs (cobalts, disciples, skirmishers) are countered by Long Range Frigates, or LRFs (LRMs, illuminators, kanraks), which are countered by corvettes, which are countered by flak ships (gardas, defense vessels, sentinels), which are countered by LFs...
To reiterate, flak -> corvette -> LRF -> LF -> flak...
All 4 of those units are beaten by Heavy Cruisers, or HCs (kodiak, destra, enforcer), which are countered by bombers, which are countered by fighters and corvettes, which are countered by flak...
To reiterate, flak -> corvette/fighter squadron -> bomber squadron -> HC -> flak/LF/LRF...
Note that while HCs may beat all those frigates, they aren't as good as the proper counter and have other disadvantages (mainly susceptibility to bombers)....for example, HCs may beat LFs, but LRFs would beat LFs better....
There is one important exception, to the above general counters, and that is that illuminators WILL NOT be counteredy be corvettes once the illuminators have sufficient numbers (this is due to the fact that illuminators shoot on 3 sides)...you will have to use HCs or fighters to kill large amounts of illuminators....
Before titans, don't get lots of capital ships unless you are Vasari Loyalists...XP is distributed amongst all caps, so you'll never get high level caps if you have lots of them...also, caps don't produce a lot of firepower, so large frigate fleets willl destroy them...you want caps to support your fleet, not be your fleet...once titans come out things change, you tend to see fleet of either HCs+fighters or LRFs+flak+bombers...people tend to go for more caps wants titans exist...
Destroy mine fields by using scouts....scouts have a passive ability that reveals all mines within a certain range....move the scout closer to the mines to reveal them, then any ship can shoot the mines...
Siege frigates are meant to speed up the bombing process after you've already destroyed the enemy fleet defending....