You should be able to play Minecraft with an Intel HD 4600 graphics core. I generally recommend a Core i5 over a Core i3 CPU because Core i3 CPUs lacks Turbo Boost which means relatively low CPU clockspeed.
Click the following link for Minecraft running on a Sony Duo 13 laptop which uses a Core i5-4200U CPU with the Intel HD 4400 (probably about 15% - 20% slower than the Intel HD 4600). The game is running at 1920x1080 resolution.
http

/www.youtube.com/watch?v=PQjfTzpqG90