I agree with everyone else... the first thing is to read as much as possible. This allows you to benefit from everyone's mistakes and experience, and this site is a great place to start. You could also watch some Youtube videos of gear lists and gear reviews to get an idea of what's out there. Visit REI, Amazon, etc (even if you're supporting local businesses) and read reviews for as much gear as you can... I find it's better to know what you're looking for before you walk into the outfitters... there at best you have the advice of a couple of people, on the internet you have the advice of thousands.

While keeping the weight down as much as possible is important, personally I don't think that's your biggest concern for your first few trips (especially if they're short ones). You won't have a great idea of what you need and don't need until after you start. My goal has always been to try and keep my weight per night at or below my previous trip. As you learn more about necessities and (if you get into backpacking more) supplement your gear with lighter, more expensive gear in the future you'll begin cutting weight. I think a good goal is to shoot for a pack that weighs 1/4 your body weight.

Buy a food scale capable of weighing to the tenths of ounces (a cheap one will do) and learn to use Excel or the Google Docs free equivalent. If you have excel I can provide you with a spreadsheet, then you enter the weight of all your gear with a corresponding checklist and play around with different configurations to find the lightest weight possible... this helped me a lot.

Learn to start looking a weight when you buy gear... I'm sure that's the first thing a lot of people here look at. 4 ounces may not seem like a lot, but if you save 4 ounces on every piece of gear you own it adds up to pounds.

Go pick up backpacking food and start trying it out at home (using whatever stove you decide on) so you know what you like. I really like Mountain House, and there are some great recipes for dehydrated food on this site.

Most importantly, enjoy yourself and the process. The planning phase should be one of the funnest.