Firstly, congratulations on making best endeavours to get this done correctly.
You are doing all the right things to avoid the pitfalls many fall in to.
Get several quotes from professional contractors
Actually read quotes and compare on details, not just cost
Get advise from independent people who understand the topic
I am not keen on contractor 1, seems a bit inflexible and wants to do it his way or not at all.
Sometimes this can lead to conflict as the job progresses, often regarding the positioning of accessories etc.
As to fitting your own supplied sockets etc, I think his attitude seems stubborn and unwilling to provide the finished job that you envisioned.
As said before, as long as it meets the relevant standards then in my opinion, it should be fitted if requested.
(As with any device purchased by the end customer themselves, the warranty lies with the person that supplied it. Not the person who installed it, providing it was installed correctly)
Number 2
Just a little concerned about the comment,
Not done network install before but can do.
Although not dangerous normally if not done correctly, if you are paying someone to install networking, you expect to have someone who has experience and knowledge required to do the job correctly.
I like the “can do” attitude of number 3
Seems to want to do the job you requested, rather than provide the job that he would like to do.
The next steps you should be thinking of are
Email preferred contractor,
If not already detailed on the quote
Specifying quantities of switches and sockets required in each room
Specifying type and quantities of lights in each room
Ensure that you agree on the heights and position of sockets, switches, distribution board etc.
Suggesting a reasonable time frame for the job to start and finish within.
Ensure that payment terms are detailed correctly
Being a short job. Days, not weeks. I would not expect any staggered payments etc.
Money up front for materials etc, would be a big NO WAY, whatever the Back story or excuse was.
Personally, I won’t pay anything until presented with an invoice detailing what I am paying.
I expect there standard payment terms for that type of job are
TOTAL INVOICE DUE ON COMPLETION
If you have never dealt with them before, I would consider agreeing with them 90% on completion, final 10% on supply of all relevant certificates.