While 128x128 "HD" skins exist, they require mods like OptiFine or Customizable Player Models . For vanilla Minecraft servers, the 64x64 PNG is the universal language of skins.
Why should you bother upgrading your skin? Because the 64x64 format allows for depth that the classic format couldn't dream of. minecraft skin 64x64 png
Use the image editing software to design your Minecraft skin. You can: While 128x128 "HD" skins exist, they require mods