Best 14'' laptop

Probably the most expensive one. Has a more powerful processor (between the two AMD ones, not too clear on the performance difference of AMD vs Intel). Has more RAM.

I'd look at a tablet if you're mostly focussed on reading research papers. Plus they can usually double up with some light browsing, games, emails, social media and make for decent note taking if you get a stylus.

To be fully honest, the market below 500 is really quite tight, as at that point there's almost no margin to be made over the cost of materials (e.g. if you look on Intel's Ark website, an i3 CPU alone, wholesale, costs in excess of 300 USD).

Really, so long as it's 16 GB of RAM, ≥512 GB SSD, and ≥1080p screen, you're getting a fairly good deal for that money - in this case I would also favour the highest spec Inspiron 14 as it's definitely worth the ~£70 for the extra performance and RAM - I'd avoid the last option as the memory is smaller (& non upgradable) and Intel tends to be extremely patchy with real-world battery life.

I go on ebay and pick up ex company machines like the lenovo thinkpad for around £350 ish. Granted you get a 12 month warranty from some sellers thats probs not worth the paper its written on, they still have a decent bit of life in them. Good memory and can often get MS Office added on aswell

You are out of luck as often there are a few flagged up on the deals section but I just looked and there isn't any at the moment.

Look for 8gb ram and long battery life. More than 10 hours on spec

Have you considered a Chromebook? (edited)