Hmmm, that's the problem with cameras: you'll never find a perfect one.
I'll echo what some of the other contributors above have said, and something they've left unsaid but is implied by their advice:
I would stick with a Nikon. All cameras, especially older film cameras, have their quirks. I have never thought that I would gain anything in general usability, image quality, and satisfaction by moving over from a Nikon film camera to any other SLR system for 35mm.
While each model of Nikon has its own foibles and "personality," overall Nikon always seemed to have the best lineup of cameras that just worked, without having any flaws/annoyances that just totally disqualified them from consideration: quality, durable, and reliable construction; good viewfinders and metering systems (mostly--your F3 has one that tends to get the most negative attention, so almost any way you go might actually be a step up in ergonomics); simple, well-placed, useful and obvious controls; great backwards and forward compatibility mostly; a huge range of excellent, professional-quality lenses and accessories at mostly reasonable prices; "consumer" cameras (like the FM/FE/FA series) that any professional could put to good use, and many did carry as lightweight but very capable backups. (One caveat--the FA, while being very advanced for when it was made, does have one of the worst reputations amongst Nikons for reliability and longevity.)
I would divide your options into either the FM series or the FE/FM3a series. Why did I put the FM3a with the FEs? Well, the FM, FM2 and FM2n have LED meter indicators and cannot shoot in aperture priority. The FE, FE2 and FM3a all have match-needle meters and aperture priority, and to me those are an even bigger difference in practical usability than whether the camera is fully manual or electronic/hybrid. I personally prefer the match-needle metering system, as you can immediately see your shutter speed and how far under/over your current settings are, for those occasions when you want to intentionally under or over expose (according to the meter) an image. The difficulty involved with this (remember, no camera is perfect!) is that in very low light, the match-needle meter becomes rather difficult to see. In low-light shooting, if you do a lot of that, you'll likely find the FM's LED meters to be much more useful. I don't use my FEs for that, so 99% of the time, the match-needle meter works best for me.
And while I really prefer to shoot everything in manual mode, having aperture priority for when it's more convenient is really nice indeed. If aperture priority is a must for you, the FE, FE2, FA or FM3a are your best choices.
As to whether you want an earlier or later version of a camera, with the FM3a, you get only one anyway. From what I've heard--I don't own one--with the FM series, the later the better; so you'd want an FM2n likely. With the FE, while the FE2 does have some improvements, the fact that you can't use it with unmodified pre-AI lenses and that you can't shoot before 1 on the film counter at anything other than 1/250 of a second (I try to squeeze as many shots as possible on a roll), and one or two other things, I chose the FE over the FE2. (I have two FEs--one chrome, and one black, as you should!) Ken Rockwell, bless his heart, actually has some really good analysis of the relative strengths and weaknesses of all these cameras compared to each other which you may find useful.
If you do go with an older FM/FE, one thing that you can do which will make it noticeably if not revolutionarily better is to swap out the finder screen with one made for the FM3a. Those screens are brighter, a bit less grainy, and seem to pop into focus a little better than the original screens. You may have to adjust your metering by using exposure compensation or tweaking the ISO if you do that, because the FM/FE's meters read light coming through the screen, but as I shoot pretty much only B&W negative film with mine, and the exposure difference isn't much (and I tend to overexpose my neg film slightly anyway), I've found no need to do that.
Best of luck, whichever way you decide to go!