Don't have a suggestion for shoes ... if you can't wear sneakers, you won't probably find anything really great. (sorry)
Steth though ... Littmann has been the gold standard for years, it's what I am still using (Cardiology II) but most of the cardiology/pulmonary nurses that I work with are going to Ultrascopes when they need to replace one. They have individualized heads, and can be engraved with you name. Would suggest whatever brand you buy, get the longer tubing - may be a bit harder to hear at first ... but if you are listening to breath & heart sounds ... and they are coughing ... you will appreicate those extra couple inches

I've suggested the following web site to some of my students for a deal (have never ordered from them ... so can't vouch for the company ... but don't have any reason to mistrust them.)
http://www.rnsupply.com/ultrascope.html