you want to look for the important stuff that will kill your hive. do you have a queen? you may not see her, but do you see eggs, or very young larvae at different stages of development. do you have a good brood pattern and does the brood look healthy. are they building up. are they building out the hive. do they have stores, or do you need to feed? take pictures. you can go back over the pictures and see if you missed anything. you can post them on here when you have questions. when i was starting out, i found so much more on the pictures than i saw when doing the inspection.
equipment: don't get carried away. as with any hobby, there are lots of neat and useless things to buy :-). i don't have a problem with used equipment. when i get it, i clean it well, bleach dip it, and change any foundation. in fact, frames are cheap and i often just change out the frames.
swapping hive equipment: if you have several hives, there will be cross contamination no matter what you do. by contamination, i mean the transfer of material from one hive to another. if you have a weak hive and need to pull a frame of brood from another, you will do it. if you have a really sick hive, you will quarantine it and not use it as a donor hive. i learned that the hard way when i swapped chalkbrood into another hive.
in all things...KISS and common sense :-D