Meat cleaver and a boning knife are two very different types of knife and not interchangeable at all! You could pick up both for not a lot of money, what sort of a budget are you thinking of? With the amount of use they will get at home you don't need to spend loads (but can do if you so desire!). A boning knife looks something like this:
http://www.nisbets.co.uk/Victorinox-Rigid-Boning-Knife-15cm/C671/ProductDetail.raction
A cleaver looks something like this:
http://www.nisbets.co.uk/Vogue-Black-Cleaver-204mm/D474/ProductDetail.raction
Boning knife is used for (as the name suggests) removing bones from meat and not a lot else (although I use mine for filleting fish as well). The shape makes it easy to guide the tip around awkward shapes and cut cleanly whilst using the tip. A cleaver is used for chopping bones and not a lot else, although in east asia they often use a cleaver shaped knife for prepping veg (although these will usually have a much lighter blade than what we call a cleaver in the west).
The two knives above cost about £20 and £25 respectively and would be more than adequate, although I think the cleaver is fairly large. You can get smaller cleavers that might be more suited to you although I would have to investigate further where to procure one from. I wouldn't spend any less money than this personally as at this level you get a product aimed at commercial use and is going to be hardy and ergonomic enough to perform well repeatedly without being expensive. Of course you can spend a lot more if you so desire and I wouldn't blame you if you wanted to (obviously I have an interest in knives

), but these will work well. Let me know a bit more about what you think and budget etc and I can guide you with some recommendations and places to look etc!