Coming in the baggage inspection is foregone, but the passports recorded again. Rafah is the entrance to Egypt, easy enough it looks, but it is not encouraged to get an Egyptian Visa from here, so if travelling alone a visa may well be refused. This can be got from Tel Aviv, for which you need basically to take one full day to arrange, or if you fly into Egypt it is issued at the Airport in Cairo. However coming back into Rafah usually the Israelis give only one month tourist visa, argument here may get you one week, or 48 hours as in one notable case of a friend. Service taxis to Cairo take 6 hours, long tiring trip, but cheap.
Bus services go from Israel to Cairo and can be arranged, also long trips but cheap.
Many of these are specialists and the good ones are well known, and will easily visit you in your house. Cost around 40-50 NIS for home visit. Prescription drugs readily available for almost any common condition. Working in Gaza is relatively simple. The working days are Saturday to Thursday.