Reddit mentions of Asus TUF Gaming Laptop FX504 15.6” Full HD IPS-Level, 8th Gen Intel Core i5-8300H (Up to 3.9GHz), GeForce GTX 1050, 8GB DDR4 2666MHz, 256GB M.2 SSD, Gigabit WiFi, Windows 10 - FX504GD-NH51

There are a few more options

1. https://www.lenovo.com/us/en/laptops/thinkpad/thinkbook-series/Lenovo-ThinkBook-14s-IWL/p/88LG8TB1343 For a similar price you get similar hardware to what you found, but a better brand laptop (and a business line instead of consumer). Should have good battery life and decent performance for school.
   
2. https://www.newegg.com/p/1TS-000A-05ZU8 It has a better CPU and GPU. Battery life won't be as long, and the SSD might be a bit slower, but it should work great for most workloads. Not sure on quality though as I don't buy much from newegg. Amazon alternative https://www.amazon.com/Dell-G3-Gaming-Laptop-G3579-5965BLK-PUS/dp/B07C9J1PY6/ref=sr_1_6?fst=as%3Aoff&qid=1568821642&refinements=p_n_feature_fourteen_browse-bin%3A2057441011%2Cp_n_graphics_type_browse-bin%3A14292273011%2Cp_n_size_browse-bin%3A2423840011%7C2423841011%2Cp_n_feature_five_browse-bin%3A13580790011%7C13580791011%7C7817224011%2Cp_n_feature_twelve_browse-bin%3A9521908011%2Cp_n_feature_three_browse-bin%3A9647486011%2Cp_n_feature_four_browse-bin%3A2289792011%7C2289793011&rnid=676578011&s=pc&sr=1-6
   
3. https://www.lenovo.com/us/en/laptops/ideapad/ideapad-300-series/IdeaPad-L340-15IRH-Gaming/p/88IPL301161 This goes a bit above your price range, but has better specs than the newegg dell even (minus SSD size) if you have ebates or something similar in the states it might offset your extra cost. SSD is a bit small though on the affordable model.
   
4. https://www.amazon.com/ASUS-IPS-Level-i5-8300H-GeForce-2666MHz/dp/B07L28M2CB/ref=sr_1_10?fst=as%3Aoff&qid=1568821514&refinements=p_n_feature_fourteen_browse-bin%3A2057441011%2Cp_n_graphics_type_browse-bin%3A14292273011%2Cp_n_size_browse-bin%3A2423840011%7C2423841011%2Cp_n_feature_five_browse-bin%3A13580790011%7C13580791011%7C7817224011%2Cp_n_feature_twelve_browse-bin%3A9521908011%2Cp_n_feature_three_browse-bin%3A9647486011&rnid=9647481011&s=pc&sr=1-10 This is similarly specced to the newegg one but cheaper. It's heavier and definitely appears gaming. Battery life will be less too.

Hey, I found this gtx 1050 laptop. It seems really good to me, but unfortunately it does not have a 1 tb hard drive :(.

I found another option, this time it has a 1tb drive but it is slightly thicker than the prievious model and unfortunately is definitively gamer^^tm certified.

No, that has a rather weak mobile processor and no GPU at all. Here's a couple decent looking examples of what to look for - these are basically as cheap as it gets without being on sale:

Latest generation GPU

Previous generation GPU

Can you afford around $650? I am in the UK so I am going onto the American version of Amazon but I found tons for $640-670. All below $700. Unfortunately laptops with the 1050 can be a bit pricey but in England we have them for around £600 on sale sometimes. But here's a good one with an i5 cpu, 1050, 8gb ram and 256gb ssd: https://www.amazon.com/ASUS-IPS-Level-i5-8300H-GeForce-2666MHz/dp/B07L28M2CB/ref=sr_1_8?keywords=GTX+1050+gaming+laptop&qid=1570097188&s=gateway&sr=8-8

Only problem is that you may have to plug in an external hdd to install some games.

https://www.amazon.com/ASUS-IPS-Level-i5-8300H-GeForce-2666MHz/dp/B07L28M2CB/ref=mp_s_a_1_3?adgrpid=57563685513&gclid=Cj0KCQjwn8_mBRCLARIsAKxi0GJz2zCv5udPQambBWgRlVz7DMi7VecGyUXXUPdh3nKRIiU4I49k1f8aAvpDEALw_wcB&hvadid=274737637366&hvdev=m&hvlocphy=9022860&hvnetw=g&hvpos=1t2&hvqmt=e&hvrand=5959151970244805640&hvtargid=aud-647006051489%3Akwd-299788589936&hydadcr=20137_9665369&keywords=1050+laptop&qid=1557437413&s=gateway&sr=8-3

Thanks for the suggestion, gives me a good basis for more research. Do you think this with another 8gb of ram added after the fact, would be a better deal for my purposes?

https://www.amazon.com/i7-8750H-Processor-GeForce-Gigabit-Windows/dp/B07L28M2CB/ref=sr_1_4?keywords=laptops&qid=1563147217&refinements=p_n_graphics_type_browse-bin%3A14292273011%2Cp_n_feature_four_browse-bin%3A2289792011%7C2289793011%2Cp_n_operating_system_browse-bin%3A17702486011%2Cp_n_size_browse-bin%3A13580784011%7C2423840011%7C2423841011%7C3545275011%2Cp_72%3A1248879011&rnid=2242797011&s=pc&sr=1-4&th=1