One other important consideration should be age. Young lovebirds are far more easily tamed than older lovebirds. I personally would recommend that you try and get a hand fed lovebird because hand fed lovebirds have already gotten use to humans since hand fed lovebirds were not raised by their own parents but by humans.
Hand feeding lovebirds is a method used to get the lovebird use to humans and to get the lovebird to learn to trust humans. Hand fed lovebirds will bond to you just as easily as they bonded to the person that hand fed them; but that doesn't mean that you will not have to work with you lovebird to keep the bond strong and the bird tame. It just means that you will have a much easier time establishing the bond and relationship than you would with a parent raised lovebird (a parent raised lovebird is a lovebird that has been raised by it's original lovebird parents)
You will want a lovebird that is between the age of 6 and 8 weeks old and has been weaned from its hand feeding formula, while lovebirds fledge in the in the wild at around six weeks old the parents still continue feeding them directly on the odd occasion. They don't kick their baby lovebirds out of the nest at 6 weeks and make them survive on their own. Hand fed lovebirds should be allowed to wean themselves on their own schedule which can vary from seven to eleven weeks old.
If you get a lovebird that is unweaned you are going to have to continue feeding the lovebird your self until it is 100% weaned; in any case the breeder or petshop should not have given you a un weaned lovebird.
In addition to being more trusting of their human counterparts hand fed lovebirds are also less noisy than parent raised lovebirds.
The best part about a hand fed lovebird is the fact that they love to cuddle and snuggle. All though lovebirds look small and delicate, as small as they are; they like to do things on their own terms, which means if they are sick of playing or sick of being petted they will often let you know by nipping you or giving a loud squawk.
How can you tell if a lovebird is hand fed?When you are in the petshop or at an aviary with a breeder, you should always ask the person responsible for the birds to let you hold the bird of your choice.
If the lovebird is frightened of you the chances of it being hand fed are very slim but if the lovebird seems confident enough to step up onto your finger or shoulder it was most likely hand fed.
You can still tame a shy lovebird like I did with my first lovebird but you must have alot of patience as it takes time and effort.