Hi, Welcome to JustAnswer! My name is XXXXX XXXXX I will endeavor to answer your question. first please understand that I am answering this question from my phone so there may be typos and spelling errors the I don't catch please forgive me in advance.
Not knowing your budget is a little bit restrictive however my recommendation being that it sounds like you're going to be hauling the system around using it outdoors is to go with abrand by a company called Mackie. you really want to buy used equipment on eBay or Craigslist. You are looking for a pair of eiither SRM 450 or SRM 350 monitors. I recommend 450's as they are more powerful and they will reproduce your low frequencies better. They are powered so that totally eliminates the need to carry a power amp with you. The V2s are a newer model and they're going to be more expensive and you don't need them for what you are doing. Ie: SRM450v2 verses just a SRM450. don't let the word monitor worry you as there are probably more bands using the 450s as main speakers than as monitors.
For a mixer, also go with a Mackie. The size will depend on your needs. They are available in anything from. 4 Channel to 48 channel. if you are not familiar with buying on eBay just look for a seller with a lot of good feedback. If you are patient and wait for THE deal & look every day or save your search you will probably be able to put the system together for under $600. For a mic, look for an old Shure SM 58 and you can't go wrong! . We are currently packing up our stage system (117 road cases into the trailer) tonight and I probably won't be able to answer follow up questionsimmediately but I will get back to you as soon as I can!