Honestly, I don't see much advantage (for foreigners at the beginning level) in trying to memorize something as "abstract" as verb stems. I mean, you're not writing a graduate-level paper on comparative morphology of East Slavic verbs, you're just trying to speak Russian without sounding like Tarzan!

I think it's probably less confusing (even though it seems like extra work) to memorize these six concrete forms for most verbs:

(1) infinitive
(2) masc. past
(3) 1st-sing. non-past (the я form)
(4) 2nd-sing. non-past (the ты form)
(5) 3rd-pl. non-past (the они form)
(6) the imperative

So, for писать, "to write", you'd learn:

писать
писал
я пишу
ты пишешь
они пишут
пиши!

And for печь, "to bake", you'd learn:
печь
пёк
я пеку
ты печёшь
они пекут
пеки!

For просить, "to request":

просить
просил
я прошу
ты просишь
они просят
проси!

For пить, "to drink":
пить
пил
я пью
ты пьёшь
они пьют
пей!

This way, you're reinforcing "model conjugational paradigms" at the same time you're learning new verbs, including consonant mutations and stress-shift patterns. To put it another way, once you know the paradigm for пить, all you need to memorize about бить, вить, лить and шить is that "they behave like пить."

And as you progress, you'll begin to realize that you don't need to learn all six forms anymore -- for many verbs, knowing only the infinitive plus the 3rd. pl. non-past will let you predict the whole conjugation correctly. For instance, if you know писать ("to pee") and они писают ("they are taking a leak"), you'll just KNOW that the masculine past is писал ("he peed"), the imperative is писай! ("go ahead and tinkle!") the past active participle is писавший ("[the ones] who have gone wee-wee"), etc. But that instinctive knowledge will come as a result of thoroughly memorizing the conjugations of more basic "model verbs" like читать (они читают).

P.S. I would guesstimate that there are roughly two or three dozen "model" conjugation paradigms for Russian verbs, but I don't think it's worthwhile for beginners to rote-memorize all of these patterns in one sitting! Rather, you'll just get to the point where you look up a new verb in the dictionary and realize, "Oh-ho, THIS particular -ать verb acts just like стать, but not like дать or ждать or вставать or писать or читать." (That's six different paradigms right there, by the way! Since all of these are basic, high-frequency verbs, it won't be too long in your Russian studies before you know their conjugational patterns by heart -- probably without ever needing to learn what their so-called "stems" are.)