Hi there Artisan,
I'd suggest a long handle type razor, such as the Lady Gillette or a Schick Krona. Neither one is very aggressive, but are still capable of delivering very nice results. The Gillette super adjustable is another one to consider because of the handle length and also the ability to dial in your comfort range. Then there's one called the Knack, with it's UK brother being named the Slim Twist.
In my daughter's case, the blade she likes in her Lady Gillette is a mild one called Crystal. I've given her sharper ones to use in the past, but the Crystal blades fit her best. She has also used the super adjustable razor with good results, but prefers her blue stars razor now. I'm not all that familiar with mild blades, but I do remember the Red Personna being a nice one.
If you like, you're welcome to try out a Lady Gillette and a few various blades. I have one in decent shape that could be sent out on the house if that interests you. Keep it if it suits you or just send it along if not. Best way to find out if this DE thing is for you.
Martin