Get everything in writing. That includes ownership %, money in, money out, who is allowed to use the place, how much they need to pay the other partners, who pays for repairs, whether to provide 'friends and family' discounts, who is allowed to sell, what happens if someone dies, how is the mortgage set up, what to do if one of you becomes delinquent, etc. etc. etc.
Money and friends don't mix. And that's mostly because people have different ideas in their head about what 'fair' means. Anything you don't have in writing, if it comes up in a disagreement, could cause a friendship-ending fight. Even if you are able to agree on every term and condition under the sun, there's still a problem - what if 5 years from now, someone decides that a certain clause isn't fair?
Imagine one of you needs to move into the condo because your primary residence was pulled out from under you. They crash at the condo because they have no where else to go. You try to demand payment, but they lost their job. The agreement might say "you must pay the partnership if you use the condo personally, at the standard monthly rate * # of days". But what is the penalty clause - is everything under penalty of eviction, and forced sale of the condo and distribution of profits? Following through on such a penalty means the friendship would be over. You would feel guilty about doing it, and also about not doing it [at the same time, your other partner loses their job, and can't make 1/3rd of the mortgage payments anymore! They need the rent or the bank will foreclose on their house!] etc etc etc
Even things like maintenance - are the 3 of you going to do it yourselves? Labour distributed how? Will anyone get a management fee? What about a referral fee for a new renter?
Once you've thought of all possible circumstances and rules, and drafted it in writing, go talk to a lawyer, and maybe an accountant. There will be many things you won't have considered yet, and paying a few grand today will save you money and friends in the future.