I am a huge proponent of traditional weight training. It has helped me a lot, and I look pretty toned now because of it.
If you have dumbbells, you can literally do a different work out routine every day, and then mix them up from week to week. You don't really need a lot of equipment, as long as you have different weight sets. I definitely recommend you work your way up to a gym membership, because it's more than just extra equipment, it puts you in a better mindset. Weight loss and exercise are 90% mindset for me, so it's absolutely crucial.
Anyway, as far as what you want to do for weight loss: Work out every muscle that you possibly can. The more muscles you hit per workout routine, the more muscles your body has to repair, which means a higher resting metabolic rate. This, of course, means more calories are being burned.
So, some things you can do for starters. For all of these things, do 3 sets of 15 reps, with very little rest time in between sets:
Inclined Hammer curls
Inclined orthodox curls
Rows on a bench/chair
Free weight bench (Vary the width of your arms on this to hit various parts of the chest)
inclined free weight bench
Push ups with arms close together (diamond pushups as some call them)
decline push-ups (arms close together again)
arm extensions with dumbells (behind the back or over a bench)
free weight bench (and also incline)
hold 6-inch leg raises
weighted sit-ups (incline for real burn)
weighted side bend
side leg lifts
squats (with weights)
lunges (with weights)
I could go on and on, but honestly, you can just google all of them. This site has nice gifs and explanation of every muscle exercise you can think of.http://www.exrx.net/Lists/Directory.html
You can look up any ones I mentioned that you don't understand. If you were to go to a gym though, you can pretty much see what most of the other people are doing. Just pick someone you want to look like, and mimic them.
For now, just pick 2 or 3 different exercises from each muscle group every day, and do the recommended 15 reps/3 sets. I guarantee it'll do wonders for you.
Also, get some light cardio in every few days.
Quick tip also: I always wondered when I started, "What weight should I use?"
Well, the answer is simply trial and error. Whatever weight you use, you should be able to do the first 2 sets completely, and struggle a lot on the last 4-5 reps of the last set. Once you can do all 3 sets fairly well, up the weight. At the start, you'll be moving up weight quite frequently if you exercise every day. Get about 40-60 minutes in, and you'll look incredible in a few months.
Try to do every exercise with weights. It gives you a measure of progress, and it's more effective. People that constantly do body weight stuff plateau quickly. You can't really increase resistance that way, especially if you're losing weight! Increasing resistance is a pleasurable symbol of progress.
Also, a lot of girls tell me they don't want to exercise because they don't want to look butch. Trust me, you won't. (MOST) women don't have the hormones required to make that happen. EVERY good looking celebrity does at least some weight training to look good. They don't look like bears.
If you think my post is too abrasive, harsh, or offensive, you're:
B) Too sensitive.
C) Not going to receive an apology for pointing it out.