Oh the rookie year! I still remember mine
My rookie year in the FIRST competition was 2002 where we had to build a similar robot to collect foam balls and place them in a goal. We had a similar idea of a U-shaped robot that would collect the balls in a conveyor belt at the front and load them into a hopper which it would raise on a scissor lift and dump into the goal.... Of best laid plans
We ended up with a similar design to yours with a two-wheel and two-caster drive. It was slow as heck and that was the only reason it was controllable. Unfortunately since half or more of your weight is over two non-powered wheels, they are terrible in a shoving match. As far as collecting balls, the feeder mechanism would continuously jam up and once we got a few balls in the hopper, it didnt have enough power to lift. - It was a rough year but by far the most memorable! I remember thinking how overwelming the whole experience was and how "outgunned" we were by other teams. The next year however (using the same drivetrain setup too - not sure how that happened) we won the "driving tomorrow's technology award" which allowed us to attend the championship in Houston.
Try to take this year as a learning experience - a practice for next year. Learn as much as you can throughout the whole process and apply it next year. Write things down as you go so you can look back on your notes later.
Now - your robot. I would stay away from the Caster-wheel idea. Since your resources are limited, try to concentrate on doing one (simple) thing really well and consistently. I think you are on track with the U-shaped chassis. Look at the kit robot chassis and try to mimic its driveline. You have all the parts to build it right now with no machining skills needed. If you are going for a transverse drivetrain (long side of the robot facing forward), look at the kit bot design and "squish" it end to end, then leave the front side open to collect balls being careful to observe the bumper rules. Rather than building a throwing robot, try to make one that can collect balls and then bring them to the other side of the field. You are allianced with two other machines in a match and chances are that one of them will be able to shoot. You guys could be a huge help by just bringing them balls while they fire them in. If you want to be more ambitious, try to make a conveyor mechanism (taking note of the height restrictions etc) that can suck in three balls and then just drive up next to the fender by the nets and just pop the balls into the 2 point nets. If you can do this repeatedly and consistently you will have an even stronger machine. The most important thing in these competitions is to be reliable. Even if you have a very basic and simple machine, if you can score a few points a match and get on a ramp, you will be a strong competitor. These competitions are designed so that no one robot can do everything so being able to do one or two things really well rather than everything with mediocraty will make for a much better performance. Remember that in the finals, if you have a tiny robot that can collect 3 balls at a time, bring them to another robot and then be small enough to fit 3 robots on the ramp you will be VERY valuable as an alliance partner. Just by having a small robot that can drive around in the elimination rounds will score an alliance 20 points by getting all the machines on a ramp.
Just remember to have fun and learn as much as you can for next year!
FIRST competitions are like pancakes - the first one is always a disaster but at the end of the day it's still a tasty pancake and you've gotta eat it! mmmmmm.... pancakes