A girly girl will want lifting gloves to avoid callouses, like these: Raw Power Women's Charger Fitness Gloves - Weight Lifting Gloves - Men's and Women's Gloves from Schiek, Altus, Harbinger, etc.
When I got started at home, I already knew some free weight exercises that would work with dumbbells. Miriam Nelson's Strong Women Stay Young
or her Strong Women Stay Slim
have good advice for getting started without a lot of equipment and she illustrates a whole-body approach that anyone can do at home.
You only need a couple of pair of dumbbells to start out with: but I wouldn't bother with anything smaller than 5 lb weights - you'll grow in strength quickly and won't use weights that light for more than a week or so. Don't buy heavier weights until you'll use them. I create Excel spreadsheet logs to keep track of weight, reps and sets. (I've attached one here in case anyone would like to swipe it and doctor it for their own use.)
If I were doing it again now, I might buy adjustable dumbbells that take olympic plate weights, like this: York 30 lb Cast Iron Adjustable Spinlock Dumbbell Set - Dumbbells
As it is, I own 10, 15 and 20 lb weights. They really don't take up much space. I keep them stashed under a chair. It will be a while before I'm ready for 25-lb weights - but even then - I can put off that purchase by simply adding another set to my routine or change up the exercise for that particular body part. There's a lot of flexibility in how you progress and what defines the next level for you.
The most gains in strength are made in the first few months. After that, it slows down.
Hope this helps, Cassie!