the zeobot is a good option from what i have seen as it comes with nearly everything you would need and would give you a good start, teaching the basics of roboteering. It is up to yourself if you follow this option or if you go it alone and use your imagination to build it from scratch.

to get sponsership you ask companies either by email, letter or going along in person. You tell them what you need from them, how it would be used and how they would benefit (their logo on your bot kinda thing). The catch 22 of sponsership is that companies usually like to see a partially or fully built robot before they sponser so that they know that their sponsership will be put to good use however it is a good exercise in persuation.