Title says it all. College student, need laptop for note taking and surfing the web
One suggestion might be to go used. See if you can find an older Thinkpad or something. Assuming you don't want to do any gaming on it.
I was faced with the same situation recently and I don't really like the idea of splashing out on laptops as they're not as upgradeable and maintainable as a desktop. I ended up getting an 8470p with a 3320M (the 1600x900 variant, too) for £140 off ebay with some probably crap SSD and 4GB of RAM in it. Threw another spare 4GB DDR3 SODIMM in it and a 120GB MX100 I had spare in it and it's been serving its purpose well. Much better than a chromebook IMO.
Look for open box Dell laptops (or any laptop for that matter) on ebay. I got my Dell e5470 for $775 with free shipping and it has an Intel 6820hq quad core i7, 8 gigs of ram, and a 500gb hard drive. Not too bad for an essentially unused laptop.
Honestly just buy the best $400 laptop you can find and used the extra money on an SSD
I boutght this thing like 3 or 4 years ago for $360 USD E1-571-6442
ive since added a 256gb SSD and another 4gb of ram and it still kicks ass
I run Oracle VM, gimp, photoshop, open office, ink scape, photoshop, as well as download my steam games through this pc almost every day. (this also ran league of legends maxed at 80 fps about a year and a half ago)
and this is all with a gen 3 i3 so your same 400+ssd comb will get you a much more powerful pc
http://www.microcenter.com/product/467971/Latitude_E6430_140_Laptop_Computer_Refurbished_-_Black
i7 8gbram 14" screen $349.99
if you can find a refurbished deal like this and add an ssd to it that would be perfect
http://www.microcenter.com/product/468417/Aspire_F5-573-55LV_156_Laptop_Computer_-_Sparkly_Silver
or this would be grate if you want new for $500
Acer Aspire F5-573-55LV 15.6" Laptop Computer - Sparkly Silver; Intel Core i5-7200U Processor 2.5GHz; Microsoft Windows 10 Home; 8GB DDR4 RAM; 256GB Solid State Drive
I say a Chromebook will best fit your needs for only school work.
Link to Acer Chromebook 15, a wireless mouse and a bag all for less than $300
Honestly just save yourself some money and worry's, carrying a gaming laptop just make's you a target.
These will for fill your stated need's nicely. - ( I'm from the UK and only know Mircocenture's are good for pricing apparently )
http://www.microcenter.com/product/467883/Inspiron_17_5000_Series_173_Laptop_Computer_-_Black_Gloss