they look like a three cross lace pattern. however it looks like you have a low flange rear hub and high flange front which means each wheels having different length spokes.
so for your first try, prob better taking to the bike shop. you will prob need 185mm for large flange hub and 189/190 for small flange hub. don't quote me though, thats just from memory.
strip them first and save yourself some cash. the right way to remove the spokes is with a spoke key but seeing as they are all rusty it would be easier to cut them with some good pliers. might be an idea to try and keep one front and one back intact for size ref.
then you can give the rims and hubs a good clean before getting them built back up. good luck if you do decide to do yourself. Its not that hard to lace them the truing is the hard part
marc