Please rethink getting a rabbit. Honestly I don't think people understand the amount of care involved because they are in a cage, people assume they are easily looked after. I have two big dogs, two cats, two rabbits, up until recently had two guinea pigs, and had a horse up until a few years ago. The rabbits have been the most hassle out of the lot. They need so much more space than people realise - none of the pet shop hutches will be big enough. As an absolute bare minimum you must have 10 square feet of floor space per rabbit - for two rabbits this would be a double-decker hutch at least 5 feet long and 2 feet wide (bigger if possible). This is on top of the exercise area that you provide - and really, a run isn't enough. Don't get me wrong, you definitely need one and it's good for general hopping about during the day, but for proper exercise you need to have a secure garden where they can run and jump in safety at least a few times a week (they run very fast and very far, and will bomb about the garden like a dog!). There are other considerations - rabbits need company for their mental wellbeing. A single rabbit will be very lonely and could become aggressive or destructive - they are very social animals and spend a lot of time grooming each other or snuggled up side-by-side. No matter how much human company they get, nothing compares to another rabbit (the same way as no amount of rabbit company would replace a human for us). A neutered male/female pair works best - neutering will cost you about £60 per rabbit, depending on your vet. They also need annual vaccinations (£25 per rabbit), regular flea/mite/worm treatments, and stuff to prevent fly strike in summer. Their diet has to be carefully managed to prevent illness because there are a lot of things they are unable to eat - and you have to get the balance of nuggets/hay/greens right. Then there is nail trimming, heat proofing their hutch in summer (they are very susceptible to heat stroke), cold proofing in winter, cleaning out (toilet areas daily, hutch weekly).... and they live on average for 6 years. When the novelty of the new bunny wears off, who will have to look after them? Personally I don't think they make great pets for children anyway - the average rabbit weighs 2kg (one of mine weighs double that) and they're not too keen on being picked up because they are prey animals. They can also kick out, and if not held correctly you risk them seriously injuring themselves by kicking out and twisting (broken spine being a possibility). Cost is also a factor - my two cost me at least £40 a month in hay, straw, sawdust, food, greens and toys (they are very intelligent and require stimulation and toys to play with, just like cats or dogs). With the right care, rabbits are loving, entertaining and rewarding, but I definitely consider them adult pets, I'm not sure why so many people get them for children to look after. Most rabbits live a miserable existence in a tiny hutch or end up in a rescue centre.
Guinea pigs make much better pets for children - you still have to be careful picking them up (they can't jump, so dropping them is very dangerous) but they are lighter and more compact, so easier to hold. They are extremely vocal (the range of noises they make is amazing - mine used to purr like a cat when she was stroked) and very entertaining to watch as they bumble about. You'd still need a large hutch (10sq feet for two pigs - a 5 foot long hutch will be fine), and it should be on a single level because they don't do well with ramps. If you attach a good size run, they will be happy as larry (put a sun cover on the run - they don't like being open to the air). They'll still enjoy the odd run around the garden if you can, but are just as happy running about the kitchen floor with some greens to munch on. If you get two girls there's no need to get the neutered and there are no annual vaccinations, but you will need to bring them inside in winter unless you have a shed you can move the hutch into. They are still a lot of work, and you would need to research them thoroughly, but a lot less work than rabbits.
It's been a few years since I've had a hamster but you can get a new kind of water bottle that has a pressure-tap on the end instead of the ball, our rabbits have them and they are pretty much silent (they sell them in PAH). You can also refil it without removing it from the cage which is handy.
If you're looking for an easy pet to look after, get a cat