first bit of advice is - many people new to the sport buy equipment and then quickly find that it's not up to the job. There must be loads of scopes sitting on shelves that were bought with good intention but ...
This is my view for the rifle: I would look for an Air Arms EV2 or Air Arms Pro Target. The former probably £600+ and the latter as little as £450. These are both proven FT rifles. There are of course others but they tend to be more expensive. What are FT competitors using? By far the commonest are the Air Arms Ev2 and Steyr LG100/110.
Scope: Big Nikko refers to the Nikko Stirling Diamond 10-50 x 60. This is available 2nd hand as the Mk1 (black turrets) the Mk2 (small green turrets) and new as the Mk3 (big green turrets) around £699. Secondhand I have seen the scopes from £250 upwards. All are good but popular was the Mk2.
What are FT competitors using? By far the commonest is the Big Nikko followed by the Leupold Competition scopes. There are, as you say, some much more expensive options.
Whilst I appreciate that £1000 is a lot it is worth saving up so as to get is mostly right at the first attempt - I think if you had an EV2 with a Big Nikko on top then this would take you a long way in the sport.
The MPR has been around for a while but hasn't really caught on in FT, there are a few about but nowhere near the numbers of the EV2.
Pellets - 4.52mm yes is the diameter. Some manufacturers offer 4.50, 4.51 and 4.53 options. These suit different barrels but it's a matter of testing to find out which best suits yours.
Bean bag, deep gun bag, pellet pouch, cleaning equipment, shooting glove, waterproof clothing, boots ....
I see that you are in Leicester. Dowry Hill is the FT club in Leicester (out by Groby Pool). Also you're not far from Purley Chase at Atherstone or Castle near Nottingham. Best advice is get along to a club say hello and ask about the kit being used. FTers usually love to talk about their kit and will, I'm sure, let you have a go.