Not really sure if i have a vacuum problem or im not getting full voltage from battery?

i have a 1993 ford probe. i recently just put in a new transmission and a new clutch. i took out the battery for about 3 weeks because ive been working on it slowly. well i finally get it back together and now when i turn my car on it goes to normal idle for the car which is offly low at about 250 rpms. it hits 250 then drops down like its going to die but then then shoots back up to 250. now i have everything connected because i checked for about 2 hours too make sure i wasn't missing nothing. so the cars battery wasn't fully charged so i through a battery charger on engine start to get it started then switched it to 12v 60 amp. i left it for about 5 minutes and the car was idling perfect like its suppose to. i took the battery off the charger and it started bucking again. so i put it back on and and it went normal again. my uncle says i have a vacuum problem but i just cant see how. i think the battery is bad and its not holding the voltage. i need some opinions ? im very tight on money