I got started with a local homebrew place, Maltose Express.
Caught a radio commercial they did about a sale on homebrew kits, all the basic equipment needed like brewpot, carboy, fermentation vat and lock, syphoning tubes, capper, etc. I'm a beer lover and it sounded like fun, so went to check them out. They were incredibly nice, talked me through the entire process, taught me how to use the gear, how to avoid beginners mistakes, how to find bottles cheap, good recipes, how altering recipes would change the character of the beer, etc. The guys were total homebrew gurus and were happy to share the knowledge. Walked out with all the gear, an excellent homebrew book and enough ingredients to do my first batch of pale ale.
Talking to them really speeded up the process. They took me right past beginners "kits" into specialty malts and whole grains. Those produce a much better beer than cheapo kits which rely on corn sugar in place of more expensive malts. I recommend other start the same way. On your own you'll probably produce some vinegar and taking classes is overkill. Getting taught by other homebrewers will be quick and painless and trading knowledge is half the fun. Homebrewers are beer lovers, they'll be happy to give you samples of their favorite brews and will want to try out yours too. Find a local store, go in and pick their brains.