Birds are fairly high maintenance pets. However, a budgie is going to be far less hastle then a cockatoo.
All the birds that`re going to `remember you` are in fact parrots by the way. Cockatiels, budgies and lovebirds are, contrary to popular believe, all species of parrot.
What type of bird is best for you really depends on the personality you want in your bird. It varies greatly from species to species (and even varies greatly in individuals). As a general rule: cockatiels are sedate and cuddly, budgies are playful and clownish (and very high energy!) with the ability to talk, lovebirds are playful and sassy. Other options include the parrotlet (another small, playful bird with a big attitude), the pyrrhura conure family (such as green cheeks, maroon bellieds and black cappeds. Very playful, very cuddly, they like to lay on their backs...). and depending on where you live the quaker parrot as well (very intelligent, good talkers, playful). In some statesthe quaker parrot is illegal. If you anticipate a need to move in the future, a quaker parrot might be the wrong choice. Birds of the poicephalus family (like senegals) can also be very good pets. They`ve very cuddly, physical birds but they have a tendency to be nervous and phobic. They need careful socialization to teach them to adapt to a variety of situations, people, things, places, etc...
The quaker is the largest of the birds I mentioned, poicephalus and pyrrhuras can also be larger then cockatiels. I believe the parrotlet is the smallest, though it may be the budgie. I`ve never seen two of them side by side.
Some of these birds have reputations for aggressive and territorial behavior (lovebirds, parrotlets, quakers). Pyrrhuras are infamous for their love of beaking, nibbling and nipping. Every species has a drawback (I adore cockatiels, but I HATE their high pitched screams. Solution: I bought earplugs). Make sure to research the pros and cons of each species you`re interested in and meet as many individuals of that species as possible.
Also be certain to buy a basic bird-care book like `Birds for Dummies` or `The Companion Parrot Handbook` to help you understand just what caring for a bird entails. Be careful what book you choose to buy as many bird care books are full of bad info. Get one that`s recommended to you or, at the least, check to make sure the book was written in the last 10 years.