I have fallen in love with Speedplay Frogs. The baseline pedals retail for $105, with some good price-hunting, you should be able to be in your budget.

I like them because there is no spring-tension and they have very good mud tolerance and reliability.

I currently wear Shimano M076 shoes. I bought them because I really like my road shoes by shimano. The fit is not the same, and I find the M076 acceptable, but not fabulous.

2nd Question: Inside, with bracing (bike on a trainer if you have one) practice clipping and unclipping. Lots. You will probably fall anyways. If this group you are riding with are people you do not mind falling in front of, go for it. If it would permanently damage your ego, wait to make the change.