Hi! I have some suggestions, I noticed you said you are willing to shell out a bit more money this time around. First, I'm sorry that you had your car broken into and your equipment stolen. That's pretty fucked up. Hope all else is well.
Onto suggestions, for gloves, I noticed you said you have small hands and you are a woman. There is a great brand out there geared towards making gloves specifically for women, called Society Nine. I cannot speak to the quality as I have never owned them, but from what I hear they are pretty decent and the price isn't too bad either. If those aren't up your alley, other gloves with more snug fits (I too have small hands) include Sabas Supersoft, Boon, and Twins. (Boon and Twins are Thai brands, but Boon gloves are definitely made with more of a western boxing profile than Twins are)
Pads: I don't know how much investment you want to put into pads, they're often more expensive than gloves. I personally a pair from Rival Boxing, But Society Nine also sell pads.
Handwraps: I personally get the cheapest one I can find from a semi-reputable source. I usually pick up Meister Hand Wraps, in white, so they are easy to throw into the washer and dryer. The ones I linked is $15 for 3 pairs. They'll last you a while, and when they wear out, just grab another 3 pairs.
I hope this helps, hope you are able to work out at home!