Have only read your initial post, OP, but that's enough for me to say please don't feel ridiculous. I was several stone overweight a few years ago, and was determined to do something about it by the time I hit the big 40. I started small - lots of walking, and then tentatively C25K, but it definitely helped wearing the right clothes. Sports clothes breathe better than ordinary T shirts or cotton tops, so keep wearing 'the gear'!
It's worth it, and you will succeed! We all find once the children are older we have more time for ourselves, look in the mirror and ask ourselves 'What happened?!' You've taken the first step, and it's a huge one, so congratulate yourself! You deserve to!
FWIW, I often see women who are clearly overweight wearing 'the right gear', and all I think is good on them. They're trying to change themselves, and I'm full of admiration for them. I lost my few stone over time, and I've kept it off (don't forget to track what you eat too) and I've done a couple of Races for LIfe since then too (just the 5k ones, and not fast, but I ran all the way!)
You can do it, OP! Take it slowly, but don't let anyone put you off. Wear what is needed to be comfortable when exercising, and ignore anyone who is rude to you. That's about them, not you!