1995 Mighty Max alternator or battery ?

1995 Mighty Max manual transmission 113000miles.
My truck has been randomly not starting "right" for months.Every so often it would sound like it was starting on a weak/nearly dead battery(turn the key and it would grind 2-3 times and then start), and then sometimes it would start and run fine. Also at night while the headlights were on it would squeal loudly the way a loose/worn belt can do but the belts were new and tight. At first it sqealed until it warmed up(10-12mins)but over the last week it has squealed almost non stop.Now this morning it didn't start at all.I got a jump and it started so I let it run for 10mins or so and the electronincs(lights/radio) started going out.I shut it off and it didn't start back.I'm waiting on a ride to the parts store and wondering should I just assume it's the alternator, I've got the old one off, or could it be just the battery.I'm taking the battery to get it tested as well.The old alternator had an excessive amount of oil on it, I'm thinking that can't be a good thing?

Sounds like alternator to me, good parts store should be able to test alt and batt both. Please post your result. Good luck!