This is your Bible. Read it cover to cover, and you'll have an excellent understanding of bar technique from pouring shots in a dive to mixing cocktails in a speakeasy. You WILL wind up breaking some or all of these rules at some point, but you need to know the rules to know when to break them. Memorizing recipes is important, but will come with experience. Technique is your number one concern.
While you're reading your book, go find a job as a barback. Bartending school is expensive and largely unnecessary. Barbacking is your apprenticeship. While you're working, watch what the bartenders are doing, ask relevant questions, (when it's not too busy,) taste beers and cocktails if you're allowed to, and make SURE everyone sees you hustle. If you bust your ass, show genuine enthusiasm, and express your desire to move up, you'll either wind up with bar shifts after a while, or gather enough experience to get a job tending somewhere else.
Being a bartender is rewarding, profitable, and generally fucking awesome. Work hard, show personality and passion, and you'll get there. Come visit /r/bartenders if you have any more questions - we might seem like miserable assholes but, we're nice, I swear!
Good luck, and feel free to PM me for advice.
There are two basic kinds of shakers: cobbler shakers, and Boston shakers. Cobbler shakers are the classic-looking 3-piece devices with a built-in strainer. You'll see these in the movies a lot. Boston shakers look like two tin cups of differing sizes, and one fits inverted over the other. These are commonly seen in high-volume cocktail bars.
People who make cocktails regularly will often prefer Boston shakers, because the pieces are less likely to get stuck together; however, they are not as fancy looking in a home bar, and you'll need a separate strainer.
A good source for supplies is cocktailkingdom.com. My favorite shaker is a set of plain Koriko weighted shaking tins. I have some random cobbler shakers around the house, and they're fine too, but I don't use them much.
I also recommend The Bar Book.
The Bar Book is another good one to start out with.
Difford’s Guide, Imbibe Magazine, and Punchdrink are all good, relatively consistent websites.
But don’t start just memorizing ounce counts from somewhere, good bars will have specs for their cocktails. Specs will change from bar to bar, and even from guest to guest. So it’s more important to familiarize yourself with the ingredients of the classics and how different cocktails relate to each other and place themselves into groups. Cocktail Codex, Drinking Distilled, and Joy of Mixology are good sources on cocktail families.