Neither foundation or concealer will actually cause spots, but they are often made with mineral oil as a base and can be hard to remove from the skin again, so if you are using them, make sure to cleanse skin thoroughly every night and tone as well to make sure you didn't miss any bits!
If you are still concerned, try using a foundation primer (try Nars or Ruby & Millie) which stops the product soaking into the skin and showing up on any raised or dry areas on the spots.
A liquid concealer is best, Molton Brown Take Cover Face was amazing, but I haven't used it since they changed the formula...Mac foundations are good for building up coverage, go as sheer or heavy as you need! A brush is best for this, and makes the bottle last twice as long!
(I'm a make-up artist and I'm prone to spots myself!)