While an aquarium can provide a safe environment for a rat with a young litter, cages are always the better option in my opinion. They provide better ventilation, slowing the build-up of ammonia in the bedding which can damage your rats' lungs, they let you hang toys and ropes across the cage more easily, and also allow your rats to fulfil their natural inclination to climb.
Some owners find that using a hutch provides a cosy home for their rats. These benefit from being modified to allow the attachment of toys and climbing opportunities.
Cage choice seems to be a very individual thing, but there are certain points you need to bear in mind.
Your rats' cage needs to be big enough to allow them to express their natural behaviour. The minimum I would recommend for a pair of rats is 80cm x 50cm x 50cm, as they not only need space to live and play, but also space for cage furniture. Within reason, the bigger the better, although nervous rats may benefit from a smaller space to begin with, while they get used to interacting with you.
Another consideration is ease of access. If your rats are a little timid, you need to be able to reach them. If the cage is difficult to clean out, you're not going to want to do it. Look for a cage with a nice big door which is positioned to allow you access to all corners of the cage and which will be easy to hang hammocks and ropes across. If you like to tip out the substrate straight into the bin, look for a base which will fit easily through any doors.
My personal preferred cage is the Liberta Explorer, a tall cage which is 90cm wide, 60cm deep and 120cm high, set upon a stand and with large doors that open to the full width of the cage. I use this as an open space without a level halfway down, but with hammocks and ropes to break any falls, and I use custom made metal shelves in the base to replace the shallow plastic trays which come as standard. There is also a similar but more solid (and expensive) cage called the Savic Royal Suite.
Well socialised rats will also be eager for your company and will enjoy living in an area you spend a lot of time in. It's best to keep them out of draughts, and also away from strong sunlight as this runs the risk of letting them overheat, and they are not an animal that enjoys a lot of sun. I also prefer to position the cage off the floor where it's easier to interact with the rats. Remember to keep the cage away from any curtains and upholstery that you'd prefer to remain intact, and out of reach of young children.
Most rats will learn to use a litter tray in my experience, especially if trays are placed in the back corners of the cage. A quick spray of perfume in the trays at first encourages the rats to try to cover the smell with their own.
There is a lot of debate as to whether wood shavings are a suitable litter for rats. Certainly sawdust and any other dusty substrate can cause sneezing. I would recommend a chopped cardboard substrate, but other substrates include hemp, 100% paper based cat litter (not clumping litter) and, depending on viewpoint, non-perfumed dust extracted wood shavings with large curls of wood. Do consider the feel of the litter for the rats to walk on. Walking on some brands of cat litter looks like walking barefoot across a pebble beach.
If you use shredded paper for bedding, please check that the edges are not sharp. I've seen some rats with nasty cuts to their feet from shredded paper.
My preference is for hanging up cheap toilet rolls in the cage, either threaded on ropes or on parrot toys. This not only gives them a soft bedding but also a lot of entertainment bedecking the cage with paper. Another fun option is to put their bedding on the outside of the cage, but positioned so that they can pull it in. A much better solution than letting them pull the curtains or your clothes in through the bars!
A range of activities and furnishings for the cage helps to keep rats fit and entertained. They're intelligent animals and can become stir crazy without any stimulation, and are also much more entertaining if they have something to do.
Boxes are the perfect rat toy; easy to obtain, usually free, fun to modify for both you and your rats, and disposable when they become too 'ratty'. Just pop an empty box into the cage, or spend some time making a rat castle out of a collection of boxes.
Use smaller boxes to hide treats or even their daily food in. Empty toilet rolls can be folded down at each end to hide treats inside.
The perfect place to sit and eat, or lie and doze. You can save large packing tubes for them, scrounge plastic pipe from road workers, make your own from papier mache around an old pop bottle, or even spend some money and buy them. They can sit in the base of the cage, attach to the sides, or thread onto ropes strung across the cage.
Rats love a hammock or two to lounge in. There are a wide variety available commercially, but they are also very easy to make, at their simplest being a tea towel with a paperclip in each corner.
Ropes are fun to balance across and climb up. You can make your own from plaited strips of (unwanted) bed sheets, or purchase them as parrot toys. Thread curtain rings on them to hand other toys from.
These are often sold for parrots or chinchillas, but will be appreciated by your rats.
Most rats are surprisingly quick to get used to moving perches or swinging hammocks.
Plastic igloos and shelters are commonly sold for small animals, and will be appreciated as a place to sleep when the temperature is lower, or when your rats get older and less able to climb.
Rats love paper. Toilet rolls are fun toys to hang in the cage, starting the roll for them so they can pull it down. Wrapping paper and tissue paper is fun either inside the cage, or within reach outside so the rats have to pull it in through the bars. They will also enjoy pulling in pages of old phone books hung on the outside of the cage.
Some rats love their wheel, others will completely ignore it. If you decide to get a wheel, look for one that is at least 28cm across to avoid putting strain on your rat's back, and for a solid wheel with no risk of trapping tails.
Make sure wheel is strong enough to support the weight of the rat; there are some wheels which are just too flexible on their spindle to support an adult rat. The makes I would recommend are the Wodent Wheel and the Silent Spinner.
Prolonged use of the wheel can bring on 'wheel tail', which is a curving of the tail over the back. This seems to be a habit rather than any physical disorder, as the rats are perfectly capable of straightening their tail when they need to balance. My feeling is that the benefits of the exercise outweigh the effect on the look of your rat, and that the rat would suffer from being deprived of their wheel.