Any vector based program would be best, but Illustrator is the best. Below are some tips that you should always think about when working on and finalizing your  artwork in Illustrator.

    Make sure that all text is in outlines:
    You can do that by going to Type > Create Outlines, or you can use the shortcut Command+Shift+O (Ctrl+Shift+O on PC).

    Expand and merge paths
    Stroke weights can change depending on user settings, so it’s a good idea to expand them and then merge them so they form a nice shape. There are a few ways this can be done depending on if you’re working with a brush stroke or the pen stroke. For the brush stroke go to Object > Expand Appearance to expand the stroke, then open the pathfinder window by going to Window > Pathfinder (Shift+Option+F9). Inside the window you see some fun little icons. If you hover over them you can see what they are. You’ll want to hit the one that says merge. For pen tool paths, you only need to go to Object > Expand and make sure that Fill and Stroke is selected.

    Clean up your mess:
    All the expanding and merging brush strokes can cause invisible shapes to form in the negative space which group with your colors. Plus with everything you’ve already done, you never know. Just go to Object > Path > Clean Up. If something was cleaned, you won’t see a message, but if there was nothing to clean, you get something that says “no cleanup was necessary."

    Gradients are no can do make flat color logos:
    It's always a good idea to have simple logos in place of Gradient ones.

    Merge 1 color logos:
    This keeps things really easy. One click is all it will take to change a logo from black to white. Don’t forget to do the clean up.

    After a lot of merging and expanding, you’ll probably see a lot of anchor points. This is easy to remedy. Just go to Object > Path > Simplify and adjust the settings accordingly. You’ll see how many points there are before and after the change in the dialog box. The less points there are, the better.

    Group like colors:
    Grouping like colors makes color changing a breeze.

    Save as an eps:
    It's also a good idea to try and save your design as a CS1.