I recently started doing this a local farmer's market and its fun and I even make a few Euro and get free stuff from the people running the stalls! I thought I'd list my kit here to help anyone out who'd like to do the same thing.
1. Something to sit on
This is the one I got, it suits me, it is small and low, but I find that good. It's also light and folds up small, If you are lugging all your stuff to where you will busk, that is essential.
2. A music stand
This one can be set low as well because if you're sitting you'll need that. Quite heavy, but it has little wire things that stop the music blowing away, you might need to bring pegs or something though.
3. Stuff to play, and something to keep them in
I've printed out songs from sites like www.chordie.com I don't play many from memory mainly because I want to know too many and can't memorize them quickly enough! I put the music in folders with clear plastic pockets, keeps everything together for me. I get them cheap in Tesco in Ireland, I'm sure you can find the same thing wherever you are.
4. A playlist?
I generally play what I feel like playing rather than have a planned list. I'd never just play the same list over and over. Id rather chop and change, and I take requests. I can find the chords on my iPhone. The muffin man asked me to play "Sympathy For The Devil" by the Rolling Stones last week. For which, I received a free muffin!
5. An Amplifier
Playing in a crowded outdoor place, you'll need it. But be careful not to be so loud people can't ignore you if they choose to. Be considerate. But also not so quiet you can't be heard at all!
I got this one because it has a strap, can take batteries, is loud enough, and you can attach a mic and a uke pickup. It's also not too heavy to carry over one shoulder. It has effects and stuff but I don't use them.
6. A microphone
I got one like this:
It had an adapter to make the jack that plugs into the amp bigger, you'll need that too.
7. A mic stand?
I stick a wire coat hanger over my head, put a kazoo on the straightened hook end, then duct take the mic to the bottom of the kazoo, so it doubles as a mic stand and kazoo holder.
8. A pickup for your uke or a semi-acoustic uke
I got one of these initially:
But it occasionally fell off, so I eventually bought a Korala soprano ukulele with a built in pickup that was about €150, plus 20 for the cable. Can't find much about these online, but I really like it, the quality is very good for the money: http://www.koralaukuleles.com/
I wasn't planning to spend that much! But the few hours I spend in the market on a Saturday Morning/Afternoon does make me €20 or so. I also get free stuff and discounts from the stall holders in the market who appreciate the music. Not to mention to the smiles and happy reactions I get from passers by, little dancing kids (I also keep a pocket of cheap kazoos to give away) not to mention just enjoying playing for a real audience.
It doesn't feel as high-pressure as playing at an open mic even: I go when I want, play what I want, for a long as I want. It's more relaxed. I find I am learning though, and getting better, or at least trying to. It's a good way to see what songs work as well: some sound OK sitting at home, but not great in public and vice versa.
Also, I bring my daughter, and a friend of hers sometimes, and it's nice to have time with her at the end of the week and give my wife a break. So, it works out all round. My daughter happily chants and browses with her friend, or just wanders around asking for requests and browsing the stalls. She swoops on any money I get and buys bits and bobs with it, but I don't mind.
OK, I'll update this post if I think of anything else to add to this!