Don't buy a bike from anywhere without sitting on it and riding it a bit to get a feel for it. Bike frame geometries vary between manufacturers and styles, and different bikes will fit you differently.
Don't be tempted to get a massive squashy saddle. This will just absorb your energy. Saddle comfort is to do with the width of your pelvic bones, not the size of your bum.
Do get some good padded shorts - either Lycra shorts, or padded undershorts to go under loose shorts.
Don't believe that women can only ride "ladies frames" or women specific designs.
A good second hand bike will be much better than a cheap new bike. Have a Google, or ask on local FB pages, to see if you have a local bike CIC (community interest company) - these are not for profit places that take in bikes, refurbish them, and sell them at low cost. They are usually run by bike geeks (that's a compliment) who will be able to help find you one that fits, can carry a toddler, meet you needs etc etc etc. Here is an example of one in York]]
Please don't buy a bike from Halfords/Charlie Browns/Wilco /Argos etc - I've seen so many badly put together "Bicycle shaped objects" in my many decades of riding bikes and coaching cycling. Having said that, Decathlon are pretty good for a warehouse shop, and their bikes are good for the money.
If you can't find a CIC, see if you can find a local bike shop. Some do sell second hand. Local bike shops are wonderful to have on side for advice and servicing.
If you want to go down the eBay/FB marketplace etc route, see if you can give a friend, colleague or someone who knows about bikes to come with you. Look for decayed tyres, bent frames, wrinkled paint work, cracked tubing, buckled wheels (you don't want any of them); look for responsive brakes, smooth gears, smooth wheels, tight steering.
If you don't mind saying whereabouts in the country you are, I'll see if I can find you a good place to start.