First off:
unless you need a dedicated GPU (say, for gaming or applications benefitting from serious hardware acceleration),
do not buy a laptop with a dedicated GPU. You'll end up paying (often significantly) more for a hotter-running and louder laptop than you need, with zero real-world benefit for your use case. Buying a laptop with a dGPU and disabling it is - pardon my French - a really stupid idea. This might be down to different terminology though - what you call "CPU graphics" is the iGPU or integrated GPU, while speaking of "the GPU" in a laptop normally implies that the laptop has a dedicated/discrete GPU (aka. "dGPU"). Which you definitely don't need, or want to pay for.
Beyond that, you're right that you will benefit from a quad core - even web browsing benefits from that. I moved from an i7-7600u work laptop to one with an i7-8650u early this year, and even for just normal office use the difference was noticeable.
You're also right that buying an i7 generally isn't a good idea unless you really need maximum performance in your form factor - i7s run hotter, use more power, and cost more. i5s usually deliver ~90% of the performance with better thermals (and thus noise levels) for significantly less money.
On the AMD side, this is less clear-cut, as the difference between mobile Ryzen 5 and Ryzen 7s is smaller on the CPU side - the biggest difference is the iGPU. Both will perform more than adequately for your needs (quad core i5 levels or slightly above), but have the benefit of a more powerful iGPU than anything Intel delivers, which is beneficial for anything that can use hardware acceleration. Power draw is roughly the same as Intel, but with lower peak draw in well-designed laptops. They're also usually relatively affordable.
Beyond that: as long as the basics are in place (suitable CPU, no dGPU, enough RAM (I'd say at least 16GB, which will likely make buying used difficult), sufficient SSD storage), physical design and ergonomics are actually what I consider the most important for a laptop. Does it have a good keyboard, trackpad and display? These three are what you'll be directly interacting with likely 100% of the time you're using the laptop, after all. Which is the most important, and what you prefer is of course entirely up to you, but you say you type a lot, so I would prioritize the keyboard - in which case nothing beats a ThinkPad. For typing, display resolutions below 1080p are also a no-go, as text rendering will be blocky, blurry or uncomfortable no matter your eyesight. And IPS display would also be better than anything TN, mainly due to TN's poor viewing angles being a significant hindrance on a laptop. You don't sound like you'll be doing very color-critical work, so you don't need to look for anything with a color-calibrated display.
As such, I stand by my recommendation of the Thinkpad T495 or T495s. The s is slimmer and lighter, but also more expensive, so for your seemingly mostly stationary use I'd go for the T495. Here in Norway, a T495 with a Ryzen 5 3500U, 16GB of RAM, 512GB SSD and 1080p IPS display is
NOK 11737 (you'll need to select the RAM and SSD yourself, everything else is stock). This might be slightly beyond your budget, but again, Lenovo has frequent sales, and a 10% rebate if you're in any way connected to an educational institution. Also, the laptop has 8GB of soldered memory with a free SODIMM memory slot, so if you can live with 8GB for a while you can save quite a bit by upgrading the RAM yourself (this is a trivial thing to do even for someone who has never installed hardware in a laptop, btw). The SSD is also upgradeable, but this is a much more involved process, so I'd buy what you need there right away.
The E series Thinkpads are also a good option, of course, and significantly cheaper. An E495 with a Ryzen 5 3500U, 16GB of RAM and a 512GB SSD is
NOK 6811.50. Do note that the E-series (at least the Ryzen 5 config in Norway) comes with an old-school HDD instead of an SSD as stock, which will be absolutely
terrible for the perceived performance of the laptop. Whatever you do, get an SSD. The price I quoted is with the "dummy HDD" and a 512GB m.2 SSD. You can add in the HDD if you need more storage cheaply, but you OS and software should always run off the SSD.
If you really want to buy used, look for any used ThinkPad with the required specs, but be wary that quite a few business laptops have terrible, low-grade TN 1366x768 panels. Avoid those at all costs. Finding a used business laptop with a quad core CPU might also be a challenge, as those are relatively new and laptops like these tend to be in service for a few years before being replaced. Also look for businesses selling refurbished laptops in your country, they might have some gems in stock.
Not a bad idea, but those tend to be expensive, and their display size is quite small. Given that the OP doesn't seem to care about portability I'd go for something in the 14-15" range simply due to the ergonomic improvements, no matter how much I like the Surface lineup. The new 15" Surface Laptop might be an alternative, but I'm willing to bet that will cost far more than a ThinkPad T495.
(Scandinavian) 
