Choosing a cage for a degu
Degus are an often misunderstood pet who are similar in intelligence to rabbits and despite their small size have complex social and behavioural needs and should be kept in same-sex pairs (or trios, 4s, etc). As an absolute minimum they need a non-plastic cage 2ft tall by 2ft wide by 1.5ft deep - you should almost definately add another ft to one of those dimensions if you are an animal lover. An all metal cage is best and mesh floors should be covered with cadboard or carpet. They will jump, climb and run all day and love shelves, non-toxic woods, ropes, hammocks (for snuggling) and a non-wire wheel. More details below...
Alot of people think of degus as being similar to gerbils - actually they are a lot closer to chinchillas, and are believer to be related to rabbits and squirrels. As an example of their intelligence, a recent study showed they could find and choose a suitable length rake to reach food placed out of their reach. If you think of squirrels, it will give you an idea of how active they are, they love to climb and jump, For that reason, height is one of the most important things in a cage - that's great for you as a tall cage is normally no more trouble than a shorter one. Do not keep a degu alone - they are naturally social animals and will be lonely. This will show as them being less active, getting ill easier and having a shorter life expectancy. If you can afford 1 degu then 2 will not be any more trouble.
The absolute minimum height you want to look at is 2 ft (24") - cages can go much taller - ours is 5ft 6" but as soon as you go over 3ft, you'll want to make sure that there are levels to break it into sections. This will stop a badly timed jump resulting in too high a fall.
For depth (front to back) I would recommend 18" minimum and for width 24" or more. Obviously, the bigger the cage you have, the more active and happier your pets will be - after all, they will be living in it almost 24-7.
It can be hard to find the bigger cages - pet stores don't often carry them as they take up so much space - you may want to go online and look - John Hopewell (search for it) (mentioned below as well) does custom cages at decent prices. Pets at Home stock two suitable cages - 2ft h by 3ft w by 18" d and 3ft h by 2ft w by 18" deep - these have a wire bottom though, so you will need to cover it (see below)
One problem with Degus as pets, is finding a cage made of the correct materials. Degus are ferocious nibblers and will eat through plastic or wood in hours - especially if they think that doing so will let them escape! When we tried to transport ours in a plastic carrier in a car, we spent 2 hours of a 3 hour journey too scared to open the boot and hoping they didn't chew through the brake lines. That means that plastic base cages won't last and can be dangerous if they escape when you aren't there.
Metal or glass bases are better - glass means that you can see what your guys and gals are up to but you need to make sure they get proper air flow (Degus can't sweat so are sensitive to overheating). If you like that style, you can sometimes get cage 'toppers' that sit on top and give a best of both worlds. The other thing you may find with using aquariums / glass cages is it is hard to attach toys and food bowls / water bottles to the sides.
Wire/mesh cages or converted avairies are often used - these are the only type you can buy at Pets at Home, for instance. These are good enough to avoid escape (if you don't get it from pets at home, you'll want to make sure the bar spacing is less than 1" (or 0.75" if you may have babies). However, with wire / mesh floors, degus often will develop a condition called Bumblefoot - this is similar to pressure sores and very painful. To avoid this, you'll need to put down cardboard, carpet or floor tiles over most of the mesh. Do not listen if you are told that wire cages are more hygenic because droppings fall through - Degus are clean animals and are much happier digging around in a bit of hay than walking on wire - they will not eat / sleep in their toilet area and you can change the bedding once a week when you clean the cage (you will want to clean it that often whatever type of cage you have).
The final thing to consider with wire floor cages is the potential for accidents - we have a very happy 3 legged baby called hoppity, who was almost put to sleep when she broke her leg very badly after getting it caught in the mesh floor. She's very agile now, but getting there cost ~£150 and much anguish / waiting by a phone after risky operation / etc. After that we ordered a cage with solid floors and made sure ours were covered at all times
All metal (best) or plastic (alright, but will get eaten in a few months) wheels are best for Degus - John Hopewell does some great, silent, metal (we use one in our bedroom) 12" wheels (which is the minimum size you'll need to avoid them overstreching their backs) but they are not cheap ~£40. DO NOT get wire wheels - many Degus have lost their legs are been killed in acciednts when they turn, especially when one is running and another nearby. If you don't want your Degus to become nocturnal, you may want to consider blocking the wheel up at night
Check out the website Degutopia (search for it) for a lot more information about Degus by someone who has made it they PHD to know...