You can simply buy any laptop with an Intel Haswell CPU which has an Intel HD 4600 graphics core. It is more than capable of playing Minecraft at 1920x1080, but you are not going to find a laptop with a 1080p screen for under $700. Below is a link to a Sony VAIO Duo 13 (out of your price range) which is used to play Minecraft with the less powerful Intel HD 4400 graphics core. 13" laptops tends to be expensive so 14" is a good alternative.
http/www.youtube.com/watch?v=PQjfTzpqG90
The following 14" Lenovo IdeaPad Z410 for $500 with an Intel Core i3-4000m which has the HD 4600 graphics core. It has a 1366x768 resolution and starts at 4.4lbs.
http
/shop.lenovo.com/us/en/laptops/ideapad/z-series/z410/
If you want something with a little higher than 1366x768 resolution and also have longer battery life, then you can consider the following 14" Lenovo ThinkPad L440 (business laptop) for $611 base. A 1600x900 resolution upgrade is $50. It is stated to have a battery life of up to 12 hours. Based on my experience with the Lenovo IdeaPad Y470 which they stated a 4 hour battery life, the L440 will likely be able to get at least 10 hours assuming light internet usage and no media playback. It has the same Intel Core i3-4000m CPU with the Intel HD 4600 graphics core. It is 5lbs.
http
/shop.lenovo.com/us/en/laptops/thinkpad/l-series/l440/
If you don't mind spending $779, then you can actually buy a gaming laptop, the 14" Lenovo Y410p. You get a quad core Intel i7 and a nVidia GT 750m graphics card. Overkill for Minecraft.
http
/shop.lenovo.com/us/en/laptops/ideapad/y-series/y410p/
An alternative to Lenovo and Intel would be the following 14" HP Pavilion TouchSmart 14z-n100 with a starting price of $480. Ignore the 13" HP laptop the AMD APU it comes with is very, very weak. Take the $95 option for the AMD Quad-Core A6-5200 Processor and a 1GB AMD Radeon™ HD 8670M discrete graphics chip. The brings the price to $575. While the AMD APU is a weaker processor, the graphics chip is more powerful than the integrated Intel HD 4600 graphics core.
http
/www.shopping.hp.com/en_US/home-office/-/products/Laptops/Laptops?SearchParameter=%26%40QueryTerm%3D*%26ContextCategoryUUID%3DjeEQxXjbj14AAAE0syxcZzOW%26Processor_facet_DTE2_laptops_dte2%3DAMD%26Screen_Size_facet_DTE2%3D%255B12.0%2BTO%2B14.99%255D%26%40Sort.TieredPricing%3D0&PageSize=15&SortingAttribute=TieredPricing-asc