Don't just use arbitrary sizes when you increase textures. Use multiples of 2. So good practice for an HD texture pack is to set the new textures to * 4 the previous size. This will keep your proportions correct.
You can keep the old upscaled image on it's own layer as a rough reference. For simple shape textures without color you can use the shape tool.
For shapes that a simple rectangle or elipse can't handle you can learn about the pen tool for pathing. Trace all the hard edges, set brush hardness and size, then stroke it on the paths tab.
For text I would try to match the font as close as you can, and use the text tool. Adjust the font size and align the new letters edges to the reference as best as you can.
For textures that are colored, detailed, and have complex shapes there is no simple way to upscale or trace them. These textures need to be redone by hand using the original as simply refrence/alignment.
You can keep the old upscaled image on it's own layer as a rough reference. For simple shape textures without color you can use the shape tool.
For shapes that a simple rectangle or elipse can't handle you can learn about the pen tool for pathing. Trace all the hard edges, set brush hardness and size, then stroke it on the paths tab.
For text I would try to match the font as close as you can, and use the text tool. Adjust the font size and align the new letters edges to the reference as best as you can.
For textures that are colored, detailed, and have complex shapes there is no simple way to upscale or trace them. These textures need to be redone by hand using the original as simply refrence/alignment.