What amp do I need to connect my old turntable to active speakers?

Small correction: if your speakers are active (with built-in amp), you don't really need a separate amp. What you actually need is just a phono preamp, because a turntable's output is too weak to feed active speakers directly. You can find cheap compact phono preamps that do the job, or if you want to keep a real amp for flexibility, get a stereo amp with a built-in phono input and connect its outputs to your active speakers.