You'll need a magnifying glass, plastic ruler, good coin reference book, bright lamp, and padded jeweler's tray (or a tray lined with soft felt).
To store your coins, you have several options:
2x2 cardboard holders.
Plastic tubes (ideal for rolls of coins).
Paper envelopes (for circulating coins).
Be sure to use special coin envelopes—other envelopes have chemicals in the paper that can change a coin's color.
Hard plastic holders (for proof and uncirculated coins)—you can get them for either individual coins or small sets.
Don't try slabbing at home, folks!
Slabs (sonically sealed hard plastic holders for individual coins).
Because slabbing costs a lot, you would have it done only to really valuable coins.