If you are new to biking and fixed gear in general, you might want to spend a little time reading some Sheldon Brown articles.

With your height, you probably want to drop by your local bike shop to see what size they'd recommend before you make any orders online.

If you are switching cogs, you do not necessary need a new chain but a couple of chain links, bike shops will sell you them for cheap.

"Good" is a very subjective term, especially when it comes to tires. Cheng Shin Tires make affordable coloured tires.