I'd say forget about babies and horses that are really unsound at 11.
What you want is a well behaved, well broke, sound horse.
Breaking a baby is extremely expensive if you compare the price with an already broken horse. Even if you think that a baby is cheaper, you'll have to pay for feed and vet care and farrier (at least for trims) for years, and then you might discover that your friend is not that friendly, that he/she can help you, yes, once a week, if he feels like doing it... so you'll have to spend more money on a real professional trainer, and I assure you that it'll be a lot of money.
11 yo and already so unsound he cannot be ridden regularly? It won't be long until he'll need regular meds for whatever pain he'll have. Think if he'll live like a normal, well cared for horse: 20 to 30 years. So 10 to 20 years of possibly expensive pain meds and who knows what else, other than... vet, farrier, food and so on.
Save money and buy something that you can ride now and worry about soundess issues as late as possible.