Car stuttering occasionally, a ton in reverse.

So, to be more specific,the car lately has been stuttering, for a long time i
was thinking it was like a gear slipping or something despite it being an
automatic. The stutter is the car like failing to give gas smoothly and will
shake the car and jumps it back. The Rpms die during the stutter as well,
then climb up again. This started happening about 2 or 3 days ago, and the
car is also struggling more than usual to start up. This isnt an all the time
occurence though. It was happening last night at around 12pm during a short
drive, then this morning at like 10ish it was driving at its usual old beater self,
but leaving the shop it was doing it again. Any reccomendations on what to
check at home first? I have most tools I would need other than heavy duty
stuff, just not the knowledge! And worst come to worst, shop repairs? (keep
in mind this car is a beater and really isnt worth more than like $600 repair to
me maximum ) :)