This app was mentioned in 4 comments, with an average of 1.50 upvotes
Don't even have to buy one. Free ones are available . I've used and liked that one. I'm sure it's not the most realistic, but it will get the basics under your thumbs. Plug an x-box controller or other game controller into your phone or tablet with an OTG cable Like this and you'll get an even more realistic feel.
Thats the cheapest way to Sim, assuming you already have a USB controller of some kind. If you just want to understand the controls, that's what I'd recommend.
For realistic Sims, of course, spend some money.
Why not just get comfortable flying a $30 quad and then upgrade to your FPV racer once you get nice a good with the cheap one? I've flown touch screen quads, and it sucks.
If you want to get a feel for what I mean by "sucks," try this. It's a really realistic simulator with your standard touch screen quad controls, and it's really, really hard to fly proficiently that way. Tactile feedback for where your controls are at is important because you don't want to have to constantly look away from your quad at your touch-screen controller.
I mean, you could always shell out for a $30 quad, get good with that, buy a $200-$250 premade FPV setup, play with that, and then build your 250 FPV racer and still be under your budget, and then you'd have two extra quads to fly around with your friends.
Just my 2c.
Edit: My bad, I didn't know you already have experience with quads. Not sure what to tell you, as I've used touch-screen-based controllers quite a bit and am biased against them as a result.
I've had some fun with https://play.google.com/store/apps/details?id=com.Creativeworld.QuadcopterFX
I like this one better and it supports cardboard/vr headsets.