Selecting which shoe to wear is a very personal, individualized decision because we all have very different feet with various widths, insteps, arches, and other attributes. For example, many nurses like wearing Nike Shox, but my foot will not even fit into them because I have extremely wide, pudgy feet. Many nurses like nursing shoes such as NurseMates, but my foot feels crushed and compressed in even their widest width.
I wear New Balance wide width shoes. I also wear SAS shoes.
As for a stethoscope, it depends on which area of practice you intend to work, as well as the amount of money you spend. You can spend less than $10 for a Prestige stethoscope that will work well, or you can spend over $100 for a Littman.
I'd advise you to hit up the shoe store in your area with the widest selection. Don't just go to footlocker and try on the more common shoes, find a store that carries some of the brands you hear about like Merrell, SAS, MBT, Chung Shi, Dansko, Keen, Birkenstock, etc that not every store will carry. Go shopping late in the day when your feet aren't at their best and if you find a pair that seems to feel good, take time to really walk around in them! And be sure to stand in the same spot for 5 or 10 minutes too and see how your feet feel.
If you believe you can get a better deal online (strongly suggest you only purchase from authorized dealers though) then do that, but really try the shoes out in the store first. Very few places will give you a refund on shoes that have been worn so be sure you like what you are getting before you are locked in.