Hi, welcome to the start of the journey!
Being lesbian won't matter so don't worry about that.
My husband and I are both a bit overweight but that wasn't a problem. Fibromyalgia I'm not too sure about but if you would be the main carer and the fibro wouldn't affect the care of the kids I think it would be ok.
You can request under 2s but most LAs have plenty of people who want to be 'baby carers' and I know mine doesn't generally place a baby with someone who's never had their own baby, though exceptions are sometimes made. I asked for under 12s with a preference for 0-8 and my first (and only as they're still with me) placement was brothers aged 5 and 6.
Renting's fine. We rent and to begin with only had 1 spare room but then moved to a bigger rented property.
I gave up work to foster and although on paper we were receiving about as much as my old wage in our fee and the children's allowance, obviously lots of that money was spent on the children so we did notice we were worse off for a while. Things improved a lot when we were made the children's long term carers as our weekly 'fee' increased by over a hundred pounds. Obviously most of the money is still spent on the children but it really helps to be able to afford trips out with them and not have to worry if you can afford it if you want to take them out to eat on the way home as you can't be bothered to cook! Ha ha!
I don't drive and the first year was a bit of a killer as I had to get them up and down to school every day by bus which was about a 2 hour round trip for me. As soon as I knew they were staying with me I enrolled them in a local school which is soooo much easier! But the LA won't mind if you don't drive, as long as you're willing to use buses etc.
You do get an allowance for equipment you need when they first come to you but generally you have to buy it first then get reimbursed later.
Generally the biggest difference between LA and agency is this the children are 'harder to place' when through an agency. When a child comes into care the LA always looks to see if they have a suitable LA carer available to take the child. If no one suitable, an agency is paid to find someone - which costs the LA lots of money so they only do it if they have to. This can mean that children with behavioural problems end up with agency carers because the LA carers have said no, or the child has been with LA carers and the carers can't cope and there's no one else. Agency carers get more money because often they are expected to deal with more issues. But, if there is a high influx of children coming into care it could just be the case that there simply isn't any LA carer free to take a child. In my LA anyway, it is rare for babies to be with agency carers.
Hope this has helped and good luck!