It goes without saying that one should learn all stems for every stem immediately as learning a new verb. However haven seen a pattern of the most common stem mutations (although grammarians can argue whetever it's an actual mutation or if it's just a completely new stem), will at least aid you finding the present stem easily, and make it easier for you to remember the verb's stem.
Ego and I have tried finding many rules concerning the passive aorist. I found one, which is far from bullet-proof, but still good to keep in mind:
The passive aorist is formed by adding
Xηκα, where x is most likely a dental plosive, such as t and θ, to the subjunctive stem which is chopped off where the stress lies.
Αλλάζω ->
αλλάξω -> αλλάχ
τηκα
What's interesting, is that verbs that are stressed on the paenult, very often get the classical -θηκα ορ -τηκα, while fricatives are involved, the fricative from the present stem is often kept.
My final advices:
1) Look out for verbs that in IE are completely irregular, as: to have, to be, to find, to see ...
(But keep in mind that είμαι and έχω are incomplete.)
2) Except very few verbs as to see, to say, etc, the aorist is always stressed on the antepaenult, so if it lacks a syllable, an augment έ- is added, though in some verbs, the Ancient Greek augment ή- is added instead. There's a list at the thread about the augment.
3) Internal augment! συν+verb is very common. (Ego has written a suberb thread about it already)
http://home.unilang.org/main/forum/view ... hp?t=11244