Posting to follow, bump your post, and offer my very uneducated 2 cents & hearsay.
I know of someone who has a rental property with a numbered company. It seams like a hassle. The main advantage, as I see it, is keeping it separate for litigation reasons.
As far as I know there is no tax advantage, even a tax disadvantage. I think the company is taxed at 50% or the highest possible bracket regardless of income. They intentionally pay out family members who do legitimate work so the company makes nothing every year.
I think their can be tax advantages but only once the company has 5 full time employees or something. I haven't googled this recently, I am pulling this out of my a$$.
The friends I know recently bought another property and didn't bother with the numbered company so I don't know if that says anything.
As far as having the company first, that would probably save you some money since you will need lawyers to change title to a company but I don't see what you can't still do it. Probably better to do it sooner rather than later because so their are no capital gains.
The people I know had some issues because they had a personal loan for the down payment of the property given like 15 years ago. Just recently, the company paid them back. So I'm not sure how all that works but something to look into. Finally, I would assume mortgage rates are higher for a company than for individuals.