First Project - Learning robot

Hello All, I've been doing a lot of reading and internet research for a couple months now and have finally worked up enough confidence to start my first project. My primary inspiration for pursuing a robotics project is to build and program a robot that is able to learn by introducing varying levels of randomness into it's processes and behavior. I think the best descriptive term here is stochastic learning. I'm very new to this and lack a background in engineering, electronics, or programming - so I will be starting simple, with a 2wd differential drive and only one distance sensor. First problem: the chasis I bought came with two motors, but they look pretty heavy duty and are rated at 6 volts. One question I have is whether I can just run and power them straight from the Uno, or if I need to purchase a motor shield. If I need a shield. Second problem: the chasis didn't come with encoders and I am unable to find anything online that will work. Do I need encoders for a first-time project? Or is it best for me to just keep it simple, since I'm not really that concerned with orientation and positional accuracy anyway. Final issue: is the Arduino Uno capable of running a program that is going to require a substantial amount of data storage and retrieval? I'm not sure exactly how much memory will be required because I haven't started on the sketch yet, but I don't want to get half way into it only to come up against the Uno's inherent limitations. For now I will continue with putting together some of the components I have and give regular updates here with progress. I'm excited to be doing this and look forward to eventually becoming a more productive member of this community.