My advice would be
1 Contact your Local authority and enquire about fostering.
2 Contact a couple of agencies and enquire about fostering.
There are pros and cons of both. You will see from replies you will get that some people are anti agency and others despair at LAs.
The reality is that it will all depend. Some LAs will be brilliant and others awful. Similarly with agencies.
My LA were in special measures two ofsted inspections in a row and were clearly a basket case. Nevertheless I made enquiries with them and they just never got back to me despite me chasing them. Clearly this was not an organisation to be a part of - at least at that time.
The other thing that influenced me was our location on the edge of a LA. This meant that if registered with a LA my placements could be a very long way from me but I couldnt be considered for a child a mile away across the LA border. With an agency I had a choice.
I have had several multiple sibling placements ironically one set of three from my LA ! who couldnt find foster carers from their own resources. Another set of three was from Hampshire (small world) and a set of four siblings from Haringey. We have also been considered for placements over a hundred miles away (sometimes children need to be placed at a distance for reasons of safety). The wider choice available through an agency has allowed us to select placements that we feel has suited our home and extended family.
It is generally acknowledged that the workload of your supervising social worker (ssw) is greater with a LA than with an agency and the turnover of staff is usually greater. I felt that at an early stage while we were newbies that we would benefit from having more time with our support network.
The big question that you need to ask is whether you will have access to the history of the placements before accepting them. Some agencies and LA take the attitude that they know best and you dont need to know everything. I was lucky in that the agency I chose provided us with the full referral paperwork for any placement and gave us complete freedom to accept or decline that placement. In the vast majority we declined because we did not feel it was a good match and therefore the placement would inevitably break down. I have spoken to many other f/c who are forced to accept placements often clearly unsuitable or if they turn them down are then punished by not being offerred further placements for many months. Your priority is your own child and family and you need to be sure anyone else you let in to your home is compatible. I have heard some truly terrible stories from f/carers both LA and agency.
Money is a taboo subject in fostering circles. Remuneration can differ enormously and there is always a fear during the application stage of asking what the pay is. This is ridiculous. You obviously need to know how much will be coming in so that you can budget. No-one expects social workers or paediatric drs to work for peanuts so why should a foster carer. Ask the question. How much will they pay you per day per child. What additional payments for birthdays/xmas,summer hols and how much holiday will you be given and is it paid or unpaid. If they ask why you are asking say that a foster carer said these were questions that should be asked (because they should !).
What do I wish I had known that I know now ? Well how about that I was entitled to paid holiday each year at my agency. They didnt tell me and I didnt claim it for two years and missed out on those two years. Thats 6k lost forever. Another f/c told me about it and I have just been granted it in year 3 !
Good luck with your journey and I hope it works out for all.