As long as you have the necessary cables, it doesn't matter whether monitor or TV.
But your budget is too low for 4k 60 on ultra, and Arma 3 isn't a good game to base expected performance of the PC.
By it being a bad game, I mean that the game programmers were lazy, and the game doesn't make good use of available resources. Even high end PCs have issues with it. Same deal with a game like PUBG.
Witcher 3 would be a better game to do this with.
You'd need at LEAST RTX 2080 for 4k 60 ultra, and that's over half your budget gone already.
PCPartPicker Part List
CPU: AMD - Ryzen 5 3600 3.6 GHz 6-Core Processor (£188.97 @ Aria PC)
Motherboard: MSI - X570-A PRO ATX AM4 Motherboard (£169.99 @ CCL Computers)
Memory: Corsair - Vengeance LPX 16 GB (2 x 8 GB) DDR4-3600 Memory (£89.99 @ Corsair UK)
Storage: Samsung - 860 Evo 250 GB 2.5" Solid State Drive (£53.39 @ Aria PC)
Storage: Intel - 660p Series 512 GB M.2-2280 Solid State Drive (£56.72 @ CCL Computers)
Video Card: Gigabyte - GeForce RTX 2080 8 GB WINDFORCE Video Card (£599.99 @ Amazon UK)
Case: NZXT - H500 ATX Mid Tower Case (£69.98 @ AWD-IT)
Power Supply: SeaSonic - FOCUS Plus Platinum 650 W 80+ Platinum Certified Fully Modular ATX Power Supply (£85.47 @ Scan.co.uk)
Operating System: Microsoft - Windows 10 Home OEM 64-bit
Keyboard: Corsair - K55 RGB Wired Gaming Keyboard (£40.32 @ Amazon UK)
Mouse: Corsair - M65 PRO RGB FPS (White) Wired Optical Mouse (£57.49 @ Scan.co.uk)
Total: £1412.31
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2019-07-09 16:57 BST+0100
This is just to give you an idea how much you actually need, it doesn't have to consist of those exact same parts.