For woodsball and scenario there is no definition or requiements for what would be considered a team.
There were two of us playing for a few years before we picked up a third regular and named ourselves. At 3 we were the smallest team in uk scenario (but with a lot of occasional associates, there were then the odd team of 2, and also two individuals that were recognized in the scenario annual of the time as teams of 1. (Though they were major characters in the uks scenario community)
Insurance is not essential. Sites insure against their liability
You can get your own personal liability & sports injury insurance, you may have basic sports insurance via your bank, you can get insured with ukpsf membership or buy specialist insurance elsewhere
Note that injury insurance won't pay out just because you broke a bone, it must affect you as per the terms of the policy, such as being unable to work for a prolonged period
I don't need to pay for injury insurance as I'm better covered at work. People with a proper job probably don't have as much cover as me, and the self employed will make a loss on day one if they get hurt. If you have anyone who is self employed then they need to check what cover they have
Ukpsf give a player membership scheme with 3 levels:
Full membership with insurance (£15)
Basic membership with no insurance (£5)
Free promotional membership (sometimes free by ukpsf, sometimes the site / event pay your £5)
There was a team membership for a while, you got a discount for a minimum number of people and a custom card. I don't think this exists anymore, the custom card certainly doesn't as you now get your card by email to print yourself (so you could customize by adding a logo yourself!)
The ukpsf are the recognized body for paintball in the U.K., the home office speaks to them on legal issues, they align with the epbf and other international bodies
Read up on them and cosndier it (£5 each a year gives the ukpsf good support)
The £5 basic membership goes to the ukpsf. The £15 goes to the insurer (it definately all went to the insurance policy in the past, I believe that it still does)
http://www.ukpsf.com/page/why-become-a-ukpsf-member
https://m.facebook.com/UKPSF/?ref=ts&fref=
You do not need to register a team anywhere.
Just call yourselves a team, set up a Facebook page to post up what you do, show photos and as a contact point to pick up extra people
Ideally go to a local site that runs walkons. With a monthly walkon you buy paint by the case at a lower rate which is probably your concern about bringing your own paint
See the 'what paintball costs link below for a summary of types of paintball and the cost structures
My original regular play was to a punter only site, the owner was not interested in charging us less or running walkons as he had a great site with plenty of punters. (Charging.less money to encourage other people to come had no business sense, and we disproved our own argument by coming back all the time and paying punter prices)
Later on we became associated with the site running an annual event and we had our own personal discount rate (it turned out that we were paying less than the Marshall discount)
Walkon paintball typically is one Sunday a month
Scenario events happen across the country with generaly one per site per year, but some do multiple events
Scenarios are either a Sunday or over a weekend but the games are not all weekend (there have been one or two 24 hour games, but some of that is also hype)
A weekend scenario is that long to justify the travel, usually mini games and activities on Saturday and a main game on Sunday
There are the occasional long weekend big events, and these follow the same formula with the main event on the Sunday. You can arrive on the Sunday if you are busy on Saturday but it would usually mean you still pay the price of a full ticket
Check out the paintball calendar, it might not have everything going on - especially local walkons, but gives an idea
Post up asking about what's on in your region and someone more local can give you a pointer
http://www.paintballcalendar.co.uk/categories
http://p8ntballer-forums.com/threads/what-paintball-costs.153010/