I'd go as far as to say if I could only get one pig or none at all, I'd get none. Social deprivation is cruel. No matter how much you interact with the pig in the ways the pig likes, you will never shrink to his/her size, get the same lungs and vocal cords, grow a cavy nose and whiskers, etc. They have their own body language, vocal communications, and physical playing that can't be replaced by another species.
I would be very cautious and keep the door closed as well as catproofing, to be safe. My two cats are great, and they've had supervised meetings with the cavies before. The cats were apprehensive at first (especially when the cavies walked up to them, stuck their noses through the grids as far as they could, and gave a bunch of sniffs), then curious. It was cute watching them sniff each other. Once Robin got in without me noticing (horrible of me, I learned my lesson), but she just sat in their cage until I saw her. I was cleaning the rest of the room and only noticed when I turned around, there she was sitting and sniffing while the three cavies stood and walked around her. However, after some time, cats get playful. Even if they aren't hunting cavies like prey, simply trying a friendly game of chase or wrestle (like they do with cat friends) can mean serious trouble for a cavy, as socal805 said. I definitely agree with that. Be careful from the start--don't wait for an accident to happen (with one or more animals paying with their health/lives) and then start being careful.
If you are a minor, please show your parent/s
http://www.cavyspirit.com/kidsandguineapigs.htm and
http://www.cavyspirit.com/adopting.htm especially this part:
We do not adopt out to children. We do adopt out to families. While a guinea pig may be designated as a child's pet, it must be incorporated into family life. The parents must be "into" the guinea pig as well as the child. No exceptions on this. The NUMBER ONE REASON for the surrender of guinea pigs at shelters and rescues is kids get bored with them and the parents don't want to deal with it. Lots of excuses are given to cover this fundamental problem. We will not adopt out to homes where there is the remotest possibility of this happening. It is also the primary reason for a very large number of animals that live out their lives in substandard care or even abuse.
I'm not trying to insult you, and you are dedicated if you've been saving up for two years. However, even if you do everything you can (reading and absorbing all this and GuineaLynx's info on gp care, buying good bedding and pellets, cleaning the cage without fail, keeping a constant supply of quality hay, looking at the veg charts for nutrients [vit C, calcium, phosphorous, oxalic acid] and planning proper vegetables, making sure you have those vegetables fresh in your fridge every day, feeding and watering, cleaning ears, clipping nails, finding good cavy vet/s and planning for annual or twice a year checkups, working on any behavior problems that may arise, separating pigs who grow incompatible even perhaps completely separating and adopting new companions for each, etc etc), keep it up with no breaks for 10 or more years (for better, worse, richer, poorer, in sickness and in health, through moving, school and other activities, leaving your parent/s for college, dorms and all their rules, roommates, housemates, jobs and job changes, gf/bfs and their animals, breakups, marriage, adopting new animals, yada yada), until you are financially independent, you need your parent's/parents' support. It is not a common minor or even college student that has thousands of dollars floating around even after saving for two years, in case of illness/injury that requires expensive veterinary intervention. Minors usually don't have their own cars right away either even after getting their licenses.
I'm supposed to be an adult and I still overlook things. Care is generally acceptable thanks to my partner helping, and me referencing these sites from time to time to make sure I haven't forgotten anything I'm supposed to do. Having fragile lives in my hands can be anxiety provoking at times.
You could make it kitty proof! Which would benifit you hugely the cat can come in your room and view the pigs which may also help him/she (cat) get used to the guinea pigs. 
