I can't say that donkeys are better than horses, but that they are different and have their own special advantages (and disadvantages). They're more economical, as they can (and should) eat lower-quality forage. They can be adopted in the US for just $125 through the Bureau of Land Management. They are very easy to train if you have patience and are willing to move at their pace and let them figure things out. Once you do get a horse, your donkey will be a terrific companion and can go along on rides with you or even carry a pack or a small rider. Mules and hinnies are a bit more of a challenge to train, because they may have the horse's more reactive nature, whereas donkeys are generally quite docile once they've been handled. I'd start with a donkey, for sure! You'll be amazed at what terrific pets they are, and with a little work, you'll soon be riding or driving your donkey.
As for stables accepting a donkey, call around first and make sure you have a place lined up in advance. Not everyone appreciates the donkey's braying, even though most jennies (female donkeys) are only vocal when in distress, hungry, or greeting you or their companions. Large stables shouldn't have a problem keeping donkeys unless there are neighbors close to the barns and turnouts.
Let me know what you decide!