The secret is to let someone else pay for all the upgrades, then buy it from them.
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Just seen a Michell Gyro SE + SME M2-9, Ortofon 2M Black, HR PSU for sale which might be of interest
Suggestions from here are not made with a sale in mind like a dealer has. I'm sorry to say this but most dealers I've ever come across are like vultures when they see your budget.
I'm probably going to get shot down for this as I never hear any recommendations for them, but I really like my Monarch turntable. Based around a Technics SL1210, it has understated looks, very solid, heavy as f--- and is pretty much plug 'n' play. Speed change is a piece of piss, just flip start lever t'other way. A bit pricey new, but a used example would leave enough change to get a really nice arm/cart.
The Inspire Monarch turntable is superb. No doubt but why spend that much on what will only ever be second to a fully refurbished Technics SP10 MK2.
You don't need to spend that budget on anything else IMO. You could put a SME5 on it with your budget.
If you want belt drive, the best I've heard is the VPI. It's expensive and belt driven so that rules me out but I've not heard a better rubber bander.
Regarding Brinkmann products, a new deck plus tonearm is sadly well above your budget. And unless you are willing to buy used, a Technics SP10 plus SME V will also lay beyond your budget.
You could buy a Thorens 124 in excellent condition for about £1.5K and that will include an arm.