I ran some looping workshops at the Halsway Manor European Music weekend. Students asked about good effects boxes to buy. Here's what I use.
I use three loopers:
My main box is a Line 6 DL4. It's an old design and only records a little chunk of sound, but I find it the most flexible, for hands-free use. It is also a brilliantly versatile delay box, with great models of lots of classic echo units.
I can recommend buying one from Andertons in Guildford. I'm not on commission but they do a good deal with great customer service and a 14-day return policy if you don't get on with the gear.
For longer loops, I use a discontinued Digitech Jamman. The current version is pretty affordable, and looks good although I haven't used it.
For weirdness, I use the Electro Harmonix Stereo Memory Man with Hazarai. Frankly, the odd name says it all… It's great for speeding things up/slowing down/flipping direction etc
To dip your toe in the water, there are lots of simple, cheap loopers on the market by TC Electronic, Boss and Digitech, but none of them let you manipulate your sounds as much as the Line 6 box.
The other way to try looping is to play with some iPad apps:
Loopy HD is cheap and there are YouTube videos of people using it to do some amazing things, although I haven't got to grips with it yet.
NOISE FLUX FX (by Adrian Belew) is worth a go. I used FLUX FX with the electric guitar on the track "Once there was a lone wolf" on Paul James recent solo album. (https://open.spotify.com/track/0RvdH2JJ7hkFF8s564fjV2).
Great for glitchy sounds.
I'm on my fifth Digitech Whammy. Very much an instrument in its own right and massively extends the range of the bass guitar (or anything else plugged into the box).
It works really well with so many instruments. At the Halsway Manor workshop, we put a cornett through it. Very beautiful.