Painting - What type of primer to use?

Hi y'all, I am in the process of redoing a room in our house that was used as a kid's room by the last residents. I have a question concerning which type of primer I should use prior to repainting. Half of the room was wallpapered, with surprisingly good walls beneath the paper. The other half of the room has a horrendous pink and purple gloss paint. The question concerning primer is...should I use an oil or alkyd based primer in case all of the wallpaper residue isn't gone? I think I have it all off but you know how that goes. I have used water based primer in all other rooms but this is the first that wallpaper was removed from the walls and I don't want it to show itself after a few weeks or so. BTW, the walls are plaster with a few spots of lightweight joint compound that I applied to correct some issues due to a built in bookcase being removed. Thanks.

Always better safe than sorry, who wants to go back and do something over. Use the oil primer.