We have had both cats and gerbils. DS's (11) love both, but by far they ineract with the cat more.
I didn't find cleaning the gerbil cage to be a problem, we used pine shavings and just dumped the whole contents of the tank in a garbage bag once a week. My local pet store, where the owner is extremely helpful, advised a glass tank instead of the plastic ones with a plastic lid that clips on,(gerbils love to chew, and even put hole in clothes) it had punch outs on top to add the tunnels etc which the kids love but I stopped using quickly, the gerbils would pee anywhere and it would drip out of the tiny holes in the tunnels - very disgusting

DS's were diappointed not to use the tunnels, but I was not putting up with that mess!! They did interact with the gerbils taking them out a lot, but besides holding them and letting them run in a confined space on the floor that was about it, and they are VERY fast so you have to be very careful that they don't get on the loose. ( My neices gerbil got loose and in trying to catch it my sister accidently stepped on it and THAT was a disaster!) Also our gerbils lasted 3 and 2 years. I thought they lived longer. We actually brought the 3 year olds to the vet when they got sick as we thought they had a lot longer to live and he said that was old for a gerbil. You also have to be careful about handling them if you have a cold, they can get sick from you.
Now the cat, is much more lovable in that you have constant interaction with them, they are always around. We just got a new kitten and it is like having a baby in some ways. As I am home when DS's are in school he follows me everywhere! I will have him neutered at 6 months, my vet will not neuter sooner. I never had a problem with a cat spraying or peeing on the floor (l always get them neutered) if they do it is usually a health problem, they use the litter box instinctively but you should also not change the location of the litter box if possible.
I have always trained my cats not to jump onto the kitchen table or counters. I keep spray bottles around and with a loud no and a spray they usually learn where they can and cannot go, but it take time and patience to be consistent. A can filled with coins that will make a loud noice when shaken could also work. My kitten just jumped onto the counter for the first time 2 days ago and I loudly shouted no and sprayed him, but to be sure I am keeping aluminum foil at the edges of the counter for a while, if he tries to jump up he will probalbly come down with the foil and it should scare him, he hasn't done it again (yet), I'm sure he will try again, but you do have to be persistent.
Good luck with your new pet!