A wheelie bin won't really be suitable as compost needs air to circulate through it. Also would be very messy getting compost out as you generally take from the bottom and add to the top.
We got old pallets from a nearby industrial estate (most of these get thrown out once delivery is made). Get 4 of them and tie together with tie wraps. Put somewhere in your back garden thats not very visible and your away. Tie wraps handy as you need to open it to take composted soil out every now and then - very cheap and easy to put back together with new tie wraps then.
As for what can go in:
non-woody garden prunings,
fruit peelings and cores,
small amounts of paper and cardboard,
Sawdust and wood shavings,
Basically don't put anything cooked in it or raw meat as you will attract rats.
Hope this helps.