You won't have any trouble with batteries for the bodies (3V lithium or two 1.5V lithium batteries), but you'll almost certainly find the cameras limiting. Your only two choices are aperture priority or 1/90 of a second for manual. The body was a step up from point-and-shoot bodies, but a very small step. It was Nikons attempt to attract people who were used to the simplicity of non-interchangeable lens cameras into an SLR system, and is extremely limited in functionality.
Having said that, the Nikon Series E lenses were very nice lenses. They were heavily derided in the day because they used plastic barrels instead of the tank-like metal of the standard Nikkor lenses, but if you compare the Series E lenses with the autofocus lenses of today you'll find that they are much more rugged than almost everything that's considered perfectly acceptable these days. The optics in the lenses were first rate, although the coatings weren't quite as sophisticated as Nikkor lenses. Just use lens shades and you'll find that the lenses are capable of images as good as any Nikkor lens.
The Series E 50mm, 100mm, 135mm, 75-150mm, and 70-210mm lenses are all recognized as excellent performers and many of them were re-created in later Nikkor lenses with the same optical formulas. The 28mm, 35mm, and 36-72mm lenses are good, but perhaps not quite as good as the other lenses in the series. (The formula for the 28mm lens, though, was used as the basis for the original AF 28mm Nikkor lens.) None of the lenses were dogs, and they've all held up extremely well over time (despite the warnings of doom-sayers at the time who assured us that plastic lenses would self-destruct in short order).
I'd say you probably have a nice collection of lenses, and you could probably find a nice Nikon FG body to compliment them if you want a body with more capabilities. The EM is a bit limited for an experienced photographer, but the FG offers just about anything you'd want in a nice, small body. (Small for a Nikon, anyway.) Personally I'm fond of the Nikon FE-2, but it's definately a step up in both cost and physical size...if you're not going to shoot Nikon as your primary system the investment might not be worth it. But don't judge the Nikon system on the basis of the EM bodies...the EM's are fine as sophisticated point-and-shoots, but much too limiting if you're a regular 35mm shooter.
Congratulations on the nice gift.