The dictionary 5000 Russian Words and The Russian Dictionary Tree use the labels Pf-awhile and Pf-begin for two of most common kinds of action-type Perfectives; they are illustrated below with the prefixes по- and за-, respectively.
Note that in some cases по- functions both as the normal Perfective and as the action-type Perfective, so that a sentence like Ћн пошёл в библиотљку can be translated as either 'He went to the library' or 'He set out for the library'.
Compare also the Perfective in Ї ужљ поговорќл с нќм об ітом 'I already had a talk with him about that' vs. the Pf-awhile action type Ћн поговорќл о погћде и ушёл 'He talked a little bit about the weather and left'.
Simple verb Normal Pf. partner Action-type Pf.  
читђть прочитђть почитђть read a little bit, read awhile
љсть съљсть пољсть have a bite to eat
игрђть сыгрђть поигрђть play awhile
спђть —— поспђть sleep a little, take a nap
гулїть —— погулїть take a little stroll
сидљть —— посидљть sit awhile
стоїть —— постоїть stand awhile
лежђть —— полежђть lie down awhile
идтќ пойтќ пойтќ set out
говорќть поговорќть поговорќть talk a bit, have a chat
    заговорќть start talking
курќть —— закурќть start smoking
плђкать —— заплђкать begin to cry, burst out crying
смеїться —— засмеїться start laughing, burst out laughing
хотљть —— захотљть want, get the desire for