OK. We can't really tell you about cost, as nurseries are private companies and CMs are self employed, and you would employ a Nanny, so they set the charges themselves / looking at competition in your area. One thing to have a think about is what it will cost you over a year, rather than solely focusing on the hourly rate..... ie, what about holidays ?.... what do you have to provide or pay for on top ? (my CMs always provided meals and anything they did that cost was covered by them - I provided nappies and wipes, just as an example, but you read on here that some CMs charge separately for meals or for activities they may go to as your ds gets older). Neither is right or worng, but compare the overall cost. Generally speaking, CMs and Nurseries will not cost you a lot different, as 'market forces' dictate they charge what parents will pay. One thing you might have to pay at a Nursery (and again this isn't universal) is for a "session" rather than by the hour - so you might be able to have th place up to 6pm each night, but only need it until 4pm. Again, generally you still have to pay for the place if your child isn't there, as the place is held for you. Sometimes people do 'term time only' places, but tend to be at a higher rate. However, you need to ask as it varies so much due to competition in your area.
Sorry, I don't know much about using a Nanny. My understanding, for one child is that this is the most expensive option - A CM may chage say £3.75 an hour, but can also get that off another parent, so will be 'earning' (before costs) £7.50 an hour, but with a Nanny, you are paying all their wages unless you can find a Nanny share.
A lot of people prefer a CM over a Nursery when their dc are tiny, as it's more of a 'home from home' than a Nursery. I've heard people say they prefer Nurseries because there is someone to cover if they are off sick, but, in my experience, it's very rare for a CM to be off sick, and even then, they do sometimes have others who can help you out. With a Nursery, a baby is stuck in the one room all day (except when they go out in the garden) but a CM has much more flexibility to take them out and about, just as you would - to the park, into some shops, to toddler groups, some even do things like swimming or music groups.
At the end of the day, it's a personal decision, and one that is often dictated by what is available in your area - I thought I'd be choosing and shortlisitng and selecting, before I had my first, but, in reality, it can be a bit dicatated by who can do the hours you want.
You can google 'Family Information Service' in your local area, and they will have lists of all the childcare available near you. It's a good starting point. Good luck 