YuGiOh Cyberstorm Access Booster Box - £53.95 delivered @ Chief Cards

There's not a "base game", you just need a deck per player and ideally a playmat (a.k.a. gamemat) showing you the zones (generally you have your own playmat each but you can get 2-player playmats which are just like 2 playmats put together).

You can buy a starter deck for about £6-11 which is a preconstructed deck and comes with a paper playmat. A lot of the new decks come with a staple (widely used / very playable) card which makes the decks worth buying. Because of this, sometimes people will buy 3 of the same deck to combine them as you have a limit of 3 of the same card per deck.

Alternatively, there's some products which come with a few decks and paper playmats like yugis legendary decks or speed duel: duel academy or speed duel: battle city which you can play with friends straight away.

There's also an app now called master duel which you can play on pc/mobile/console which a lot of people are enjoying and it's made them want to try out the TCG (the irl game outside of asia). It's not something to worry about at this stage but just know that the banlist (cards limited to 0, 1 or 2 in a deck instead of 3) is different between master duel and the TCG so you can't play exactly the same decks.