If you don't want to give up on graphics, but Minecraft does not run that good on your computer, well, I can make your game SUPERFAST!~
This modpack will ensure you have a somewhat optimized and a decent looking game, while being able to play multiplayer... but well, do not expect miracles or something complex, I originally made this for myself.
It uses several optimization mods (like FerriteCore, ModernFix, etc) for each versions, and some mods that add graphical impromevents (without impacting performance), so I bet this one could run well on your computer.
Make sure to go to the files, choose the version you want, and read the changelog, because it may all be very important for you to use SUPERFAST correctly, as each version can be slightly different.