I think then I would really prefer prebuild, my last years were ridden with technical issues, and it would be the first system I build myself. I like the idea of a possibility to upgrade too because right now money is tight and the need for a pc is urgent, but I should make some money soon.
Fair enough - if you plan to upgrade / tinker I would advise avoiding certain manufacturers such as Lenovo / Dell (Alienware) / HP (omen) / Acer / etc. - they sometimes do not make things as easy to work on or change as standard ATX cases / motherboards / power supplies will let you - they will usually offer longer warranties in some cases (but you are paying for it to a certain extent - nothing comes for free).
Usually I play very long sessions, and in that case I feel like a laptop will always have overheating issues, especially when its not specifically made for gaming.
There probably are some decent gaming laptops out there that can maintain a decent performance level, but higher performance output generally means needing higher performance cooling - if that's not there they will definitely throttle.
800€ is a firm limit optimally It would be between 600 and 700 but from the systems you linked so far it seems far fetched.
I am currently living in Belgium, close to the Netherlands, with family in Germany, from what you say one of these might have an advantage which is why i listed all of them.
Again, you should see if there are any forums or reddits or something that discuss best places to get stuff for where you are.
How close to the Netherlands? Some quick google searches would lead one to believe that prices / purchasing options there are a little better than in Belgium - i.e. potentially more retail options to choose from, if close enough to simply 'hop' across the border then worth keeping options open. In terms of mail order options there probably isn't much difference.
2. I mainly play League of Legends pretty much 99% of the time, but I tend to stream/record to review. The only other games I have played recently is FIFA 13, and Guild Wars 2. And, I rarely use some Adobe products like Premier or Photoshop. I haven't bought a new game in years, and so far there is nothing that peaks my interest that would need more performance.
7. Yes, I have pretty much everything leftover (Monitor, mouse, keyboard), I only need a PC and that is all the budget is for.
Based on that usage, and likely to not be a popular opinion among some of the others here, you could / maybe should aim to go with a modern platform (such as AM5 or LGA1700 - definitely no reason to go AM4 or older Intel LGA1200 which have reached end of line) and get most cost effective CPU power you are getting for the money - for those games listed you could absolutely just use current gen integrated graphics from either Intel or AMD to get by (although you'd probably have to avoid max graphics settings when it comes to Guild Wars 2).
This would give you much better headroom in terms of upgrading later on having a platform where newer CPUs could be added and graphics cards are less likely to be bottlenecked - something you'll probably want to do when you start playing games that are made since 2020.
Seeing as you all you need is the base unit and no other accessories (although hopefully your monitor has at least got HDMI or DisplayPort), you should be able to buy in to a more modern platform with your budget.
Pretty much every LGA1700 or AM5 CPU bests the AM4/LGA1200 offerings at every level, apart from the X3D chips which are both expensive (comparatively) and not great outside of gaming.
Taken from the TPU Ryzen 9600X review (and trimming the graphs):
For gaming the Ryzen 7600 / Core i7-12700K/i5-13600K are usually within 10% of the top scores without X3D cache - even the AM4 8-core 5800X3D averages out no better than AM5 6-core 7600 (non-X). The same is sort of true for Adobe Photoshop, although the LGA1700 Alder Lake CPUs (12xxx) seem to take a bigger hit compared to the Raptor Lake (13xxx) CPUs:
An AM5 platform with a Ryzen 7600 CPU would definitely offer a platform with good upgrade potential - LGA1700 is obviously competitive but no future upgrades and if you chose to upgrade from a i5 to a high end i7/i9 part later on then you gain effectively a lot less vs the amount of heat/power usage also.
EDIT:
UK pricing of the following components comes in just over £600 - they aren't even the cheapest / best value for money choices - my point there being this should be doable to get that level of performance / parts within the €800 budget (it will be tight though):
AMD Ryzen™ 5 7600, AM5, Zen 4, 6 Core, 12 Thread, 3.8GHz, 5.1GHz Turbo, 32MB Cache, PCIe 5.0, 65W, CPU
£179.99
32GB (2x16GB) Corsair DDR5 Vengeance Black, PC5-49600 (6200), Non-ECC Unbuffered, CAS 36, XMP 3.0, 1.4V
£99.49
ASRock AMD B650M PRO RS WIFI, AMD B650, S AM5, DDR5, PCIe 4.0, 3x M.2, ax WiFi/2.5GbE, AMD EXPO™, mATX
£144.98
1TB WD Black SN770 M.2 (2280) PCIe 4.0 (x4) NVMe SSD, 5150MB/s Read, 4900MB/s Write, 740k/800k IOPS
£57.59
750W Corsair RM750e, PCIe 5.0 Fully Modular, 80PLUS Gold, Single Rail, 62.5A, 120mm Rifle Bearing Fan, ATX 3.0 PSU
£89.99
Montech AIR 100 LITE Case, Black, MicroATX Chassis w/ Tempered Glass Window, 2x 120mm Fans, MicroATX/Mini-ITX
£34.99
I'd leave it to you to decide if iGPU would be up to the task:
Can't find anything useful for GW2 on AM5 iGPU - that said the Ryzen 3200G could pull solid 40fps which the AM5 iGPU *should* be able to match / beat depending on scenario.