I read somewhere that a triplet is more increased difficulty over a two-place tandem than a two-person tandem is over a single. I have found this to be true.
This isn’t to dissuade you, but to help you get your mindset in place before the first ride.
Unless you go really really cheap, you won’t find a low-priced triple the way you can find screaming deals on tandems. You’re unlikely to find a nice one under $2000 or $2500. I bought really really cheap and am happy, but very few tandemistas want a bike that’s not much good for more than puttering along a bike path a couple times a year.
If you want to really ride it, there’s likely no substitute for spending a bit of money here.