At start of game the fastest missions are generally run by the KR, by virtue of it's phaser's and transporters, but depending on the front (Gorn or ISC) the BH would be a better choice since it is more survivable against plasma hits.
Technically mid era starts pretty quick and the KRC turns up soon after. Better shields, more transporters, and more plasma and swivel mounts (plus the extra phasers make for crippling alphas).
SPF comes out next, and against non drone AI is a good choice. Some skill is required if you are going to battle drone AI because you have to deal with them every turn. BUT you have to be careful all the time because you become a sitting duck while recharging.
Slide on into the SPF+ when it comes out 6 years later. Perhaps upgrade to a CH when they come out, but only if you don't have to pay for your PF's through the nose.
Once the AI get X-ships pack up and go home.
Times - assuming a useless AI who's only contribution is to tie up one of the AI for 2 turns. When driving a small ship it is most likely to get another small ally ship and therefore usually unable to move and charge properly - drone bait. With the KRC the enemy will be larger but it's pretty simple to alpha cripple one and get the other to chase you while slinging plasma to the rear. After 5-7 min both should be crippled and able to be captured, UNLESS the odds are such that you draw DNE's - pack up and go home. 8 min missions?
For the small maulers, it's a matter of risk and how fast you want to go. Force the AI to weasel, get behind him and pound away, but with no phasers (needed for PD) no ECM, and no reinforced shields. Dangerous but deadly if the allied AI dies quickly - too many drones come at you and you are moving dead slow. 4-5 minutes if all goes well.
Against a plasma opponent, it's easier but slower because you have to wait for the plasma to be fired, then get in and pound away before they can reload. Your AI helper will probably stay alive a little longer so life is not as dangerous. 5-6 minutes simply because of the timing issues.
But I also think that half the time your AI ally is going to be a dud and do nothing useful at all, and then there will be the 15 min horrors where both enemy ships come after you and your ally dissappears in a quick ball of flame. This is one thing you will not get with the KRC/S because you win when they chase you. 10 min even when it's two against one.