Use overdose on larger maps, such as most payload maps, where the slight speed boost will make a slight difference (not much) and on smaller maps such as koth, go with stock syringe, the extra damage from the needles will be more useful than the movement gained. on smaller maps, you will have no extra speed by the time you reach the 'battlefield'
medigun / kritz is dependant firstly on map, more uber on payload for example where you need to be gaining ground all the time, and more kritz on koth where it is more a death match type fight.
I would recommend the ubersaw, medic doesnt do hardly any melee (not if you want to live) but when you do it is good to get that 25% uber from it. only switch to vita if you find you are dying a lot and have say 4-5 deaths without reaching a charge. only ever melee when you need to, always try and avoid a hand to hand, keep a distance between you and your enemy and use needles to aid your escape in dire situations.. never ever melee a spy, you will not win, they have the advantage, you may get a kill 1/100 times, but its not worth the risk. never chase an enemy while alone as medic, even if you know they have 1 hp, always run away.