Depends on how deep the pockets are mate, sim racing can be done as cheap or as expensive as you want. Just be prepared that things can get very expensive very quickly.
Rig - I'd suggest just investing in 80/20 Alu extrusion rig, they are just so stiff and modular, start off your build with a strong foundation. You can get a decent setup for around £400, something along the lines of Simlabs GT1 Evo or Trak Racer TR80 (comes with adjustable runners and sidemount brackets for seat). With both you will still require a seat, you can either get bucket seat which can be had cheap enough (I got a barely used OMP TRS-E for £100) or just pop to the local breakers when the current situation blows over and grab a cheap car seat with its runners.
Wheel, I'd look at the Thrustmaster t300rs as an absolute minimum, belt driven and interchangeable wheels, TS-PC is even better if you can find a good deal. I dont have much experience with fanatec but they are highly regarded, but come with a hefty premium to boot. Direct drive wheels are a lot of money and require a decent rig to handle the forces, also a steering wheel will more often than not need to be purchased separately and can at times be just as expensive as the wheel base itself, if not more. However if you are interest in direct drive, have a look into Sim-Plicity, Very very competitively prices wheelbases, I've recently paid ~£620 for the SW20 V3, long wait but at that price its a ridiculous deal! but as I say you also have to factor in the price of a rim.
Pedals - in my opinion the most important part of the build, if you are going to splash out cash this is where I'd be directing it at first. Three pedals are not a necessity but helpful, however Load cell IMO is. Loadcell really is a game changer, Lower end offerings are Thrustmasters T-LCM or Fanatec CSL Elite LC, if you have more money to spend though you have Fanatec Clubsport V3, or even better Heusinkveld Sprints/Ultimates.
Shifter - I havnt got much experience with H patterns other than the standard Logitech one, which wasn't that great. I dont tend to drive many cars that could make much use of an H-Pattern.
Sequentials though are great, I'm running a TM TSS Sparco Mod Sequential/Handbrake, Majority of the time it lives in Handbrake mode though as I tend to paddleshift as I race GT or rally cars most of the time.
Other things to think about.
- How are you viewing? VR, Single or Triple screen? VR cannot be beaten for immersion, but it can be a hassle using the headset every time you want to race, I also find it quite warm and and restricting in summer months and in long races. Single screen you'll want something with reasonable FOV, ultrawide or something. Triple screening will be mighty pricey but will give you the immersion without cooking with a VR headset.
- What racing platform you planning on using? AC/ACC, PCars2, AMS/AMS2, iRacing, Raceroom Experience, Dirt Rally 2.0??? Most of those title can be had for relatively cheaply with all DLC packs through sales or CD key sites and such. However iracing and to a lesser extent raceroom can be ludicrously expensive. IRacing for example requires a monthly Sub plus you need to pay 11-15 quite per track/car, and the base content for both isnt exactly overwhelming.
AC/ACC have the best FFB and physics in my opinion however are more of a hassle to find a good clean competitive race online, which is where iRacing is a better choice.
- Button boxes, something to look into as some of the sims have a lot more functions than can be configured to the buttons on your wheel. Button boxes can be really helpful, something with a few push buttons, and a few encoder dials should cover most eventualities