Basically you need to find an old workstation or micro tower that is implicitly not a small form factor PC. These typically come with power supplies that are ready to accept larger GPUs like you seem to want.
Still, cards like the GTX970 require PCIe power connectors. You need to make sure the PC you get has the appropriate ones for the GPU you intend to install.
Now, sadly there is an entire industry dedicated to snatching these up, adding a GPU, and then re-selling them as 'gaming' PCs. You could just pay the premium and pick up one of those. Or hit up the used market for discrete components (recommended if you are a really tight budget)
Here is a pretty low end one on Amazon:
Or you could see if you can track down some CPU/Motherboard combos. Memory and storage have never been cheaper, so you can always stick to new for that or low ball people on ebay.
Not what I would necessarily pick, but people do have them out there:
Find many great new & used options and get the best deals for Asus LGA1151 Motherboard Intel i3-7100 3.90Mhz TP-Link Archer Wi-Fi M.2 PCI-E at the best online prices at eBay! Free delivery for many products.
www.ebay.co.uk
Seeing 1050Ti out there for about £35.
But even so, with just a little more money into it, all new entry level parts. Just have to track yourself down a GPU.
PCPartPicker Part List
CPU: Intel Core i3-10100F 3.6 GHz Quad-Core Processor (£52.99 @ Box Limited)
Motherboard: ASRock H470M-HDV/M.2 Micro ATX LGA1200 Motherboard (£59.84 @ NeoComputers)
Memory: Corsair Vengeance LPX 16 GB (2 x 8 GB) DDR4-3200 CL16 Memory (£33.99 @ Amazon UK)
Storage: Samsung 980 500 GB M.2-2280 PCIe 3.0 X4 NVME Solid State Drive (£23.99 @ Amazon UK)
Case: Deepcool MATREXX 30 MicroATX Mini Tower Case (£35.47 @ Scan.co.uk)
Power Supply: Gigabyte P550B 550 W 80+ Bronze Certified ATX Power Supply (£51.91 @ Amazon UK)
Total: £258.19
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2023-07-31 22:18 BST+0100