I use cloth with my twins - I have some onelife and totsbots that someone gave me and I bought some terries too. The terries are great, I use them most of the time cos they are very easy to wash and quick to dry. I use onelife only at night or if we are out and about (less fiddly than terries). They have grown out of the totsbots. The terries are not so reliable for newborns cos the poo is so runny! But I rarely got poo on clothes, just on the wrap, which I can live with (just wash the wraps with the nappies). I use Motherease rikki wraps with the terries.
I totted up the other day for someone expecting twins that you need 48 nappies for twins to wash every three days. You can wash every other day but I would find that too much cos of all the other washing I have. I would have to use the tumble dryer if I was washing that much, and I don't like to use it cos of cost/environment.
So for triplets I would buy around 70-75 nappies based on them wearing five to six nappies a day and washing every three days (you need four days' worth because they will take one day to dry IYSWIM). You will need ones that dry quickly, but I am not sure which are quickest to dry. Well, I bet it is terries but they are not for everyone!
The cost saving is not as much as it is for a singleton because you have to buy three times as many nappies ie you can't use the same 20 nappies on baby 1, baby 2 and then baby 3. So if you are having no more children after these three you won't see that 'next child' saving. But lots of nappies have a good resale value so you should get some money back for them at the end.
Triplets are going to be a lot of hard work (obviously!), I mean twins are hard enough, and cloth will be quite a challenge, esp at first, but I think when you get into it you will be glad they are in cloth. I am glad mine are. Good luck and congratualtions!