All the more reason I wouldn't settle on a keeper as your first - all games you'll tire of eventually and want to swap out and if its one you don't want to part with you'll be stuck with it. It sounds counter intuitive, but with a small collection you're actually better off with games that you won't mind moving on, that way you'll get to play and sample and enjoy way more over the course of time.
To be fair, it does depend on how many pins you have on site locally.
I have Pinball Republic, Chief Coffee and Funland within cycling distance, and we’ve done a couple of train trips to The Pinball Office.
I’ve rated 75 pins on Pinside, and played a lot more, over the last year, and I don’t really want to keep swapping things in and out. So, my collection is ‘stuff I liked enough that I’d like to play it daily at home’. I can imagine, at some point, I might get good enough at pinball that these pins stop being a challenge, but I deliberately chose stuff that was notable for providing a challenge.
My last, and by far favourite, pin was Lord of the RIngs and I loved the number of modes, the variety and especially the journey it took you on.
I'm not sure yet but from what I've seen it seems like these have deep gameplay with (many?) more modes and things to do compared to Stern games, and also seem like they take you on a journey.
I’ve played multiple modern Sterns (with the exception of Elvira) and several JJP games (The Hobbit, GnR, WOZ, Dialed In). I also own LoTR.
My personal feeling is that several of the modern Sterns give the same level of theme immersion as the JJPs and are cheaper. So, I’d strongly recommend (especially as you’re interested in League) playing Keith Elwin’s Jurassic Park and Avengers Infinity Quest.
Jurassic Park, especially, has all the tension of driving through paddocks, trying to save staff from hunting dinosaurs, and flinging a tranq dart under pressure. Once you get a game going, it’s absolutely gripping, and has some amazing shots. The Premium edition, with the moving T-Rex, is above your budget (about £9k), but you can pick up a Pro for about £6-7k, which has most of the gameplay, and add lots of aesthetic mods.
Avengers Infinity Quest has some of the most complex code of any pinball machine. Although playfield toys are notable by their absence, the ramp shots are amazing, and it also has a strong feeling of playing through a film by trying to defeat various bad guys to retrieve the infinity stones and defeat Thanos.
JJP pins have a lot of fans, but my personal feeling, having played them, is that they’re very very physically pretty, but they’re overrated in terms of gameplay relative to the cost. Dialed In is a great fun modern reimplementation of a System 11 like Earthshaker or Whirlwind, Wizard of Oz is an orgy of toys with pretty average gameplay, and The Hobbit feels somewhat too complicated for what it is. I had fun playing Guns and Roses once Chris explained the rules, but it isn’t exceptional gameplay-wise - it’s just some way above average and a dream pin for Guns and Roses fans. As with all these things, this is a personal opinion, but I would definitely try some of the modern Sterns (there are a lot about onsite) before trying to track down JJP pins that are pretty rare in the UK.