Only standard copy paper, huh? In that case my answer will have to be:
Pen: Any Pilot with the #5 Soft Medium nib (as found in the Custom/Custom Heritage series pens. Not the Pilot Falcon/Elabo soft nibs.) The #10 nibs in the same series are perhaps even a little nicer in writing feel, but I dislike the larger bodies the #10 nibs are installed in (e.g. Custom 912). I prefer the size of pen bodies fitted with the #5 nib (Custom 74, Custom Heritage 91) and thus I give the overall edge to the #5.
Ink: Sailor Sei-Boku
Why this combination is my favorite: the slight softness of the nib provides a brush-like, gentle cushioned feel when writing. I write with a very light hand, so I don't usually get any line variation whatsoever, but the soft writing feel of these nibs is still noticeable and very relaxing. With this ink, the Pilot #5 soft nibs are very smooth with just the barest hint of feedback - I'd describe the feeling as being like skimming on oiled silk, not quite glassy (which I dislike as glassy smooth tends to feel uncontrolled especially during fast writing).
This sounds like a perfect combination for those who want just a little feedback for control instead of the buttery/glassy feel. I find this to be common with Asian pens because Asian writing requires feedback to get the strokes just right.
The Sei Boku ink has a nicely lubricated wet smoothness without being too wet. It gives a wonderful velvety feeling when writing, and is capable of taking the harsh edge off of even rougher steel nibs, but with the Pilot #5 soft nib, it is just heavenly. On copy paper, it holds together well and maintains good crisp line quality. On better paper, of course, this ink shines even more (it has good shading and a lovely sheen, for instance). Sometimes you can even get it to sheen on copy paper. The icing on the cake is that Sei Boku is a very appropriate ink for professional applications, and is fully waterproof to boot. No worries about smudging from sweaty palms and coffee rings = extra peace of mind.
This pen/ink combination is so comfortable for me that I often find myself disappointed that I don't have more things to write upon finishing a writing session. It doesn't matter if I've written two pages or two dozen pages; I keep wanting to write more and never stop just because it is that comfortable. Currently, the Custom Heritage 91 with Soft Medium nib is my main work pen, and I doubt it could be displaced from that position any time soon.
I totally agree about Sei-Boku. If I could only have one ink for some horrible reason like the zombie apocalypse, this would be the ink I'd choose. It is the most reliable, permanent, and a beautiful unique color as well. You are wise not to put it in your Parker 51 or any vintage pen because I've had trouble getting it out of several of my pens and it has stained a few converters. Nevertheless, amazing ink that is totally reliable when you want beautiful permanent ink.
There is, however, a second combination which I prefer over the above only in certain specific circumstances -
Pen: Parker 51 Special with fine octanium nib
Ink: Pilot Blue-Black
The main attraction of this combination for me is that I find the Parker 51 to be the most accommodating pen when it comes to pausing for thought with the pen in hand, uncapped. Sure, my Pilot 91 is no slouch in this department, but the 51 can sit uncapped for 10+ minutes and continue on with nary a sign that it has been left uncapped - no initial skip, no startup dryness, not even a dark first stroke indicating evaporation from the nib slit.
I used to not like the 51 because I prefer nibs with some softness to them, which the 51 cannot provide. But over time, I've come to realize that the relaxation afforded by the peace of mind of not having to worry how long I've kept the pen uncapped helps a lot when performing slow writing tasks - journaling, writing the first draft of a document when the ideas just won't flow, and so on.
(I do realize this is somewhat different from your request to focus on the writing feel of a nib, but since it is part of the writing experience, and in this case it is the decisive factor that makes this combination so nice and relaxing in use, I thought I should write about it nevertheless.)
My choice of the octanium instead of gold nib in the 51 is probably influenced by luck more than anything. My 51 special happens to have a particularly nice and smooth nib, which has not yet been surpassed in smoothness and writing comfort by any gold 51 nibs. There are people who claim that octanium 51 nibs are smoother writers than the 14k nibs across the board, but I will refrain from making such a general statement since I don't think the sample size of 51s I have used is large enough to merit generalization.
I've heard this claim too several times and it wouldn't surprise me. I have a lot of 51s (all 14k) and they do vary in smoothness, about half of mine are glassy smooth writers if you hit the sweet spot just right.
The choice of Pilot Blue-Black in the 51 is a "next best thing" choice, since I prefer not to use Sei Boku in my 51s. In all likelihood it's safe and I'm just being paranoid, but I still don't dare to use a nanopigmented ink in a pen that has such a large ink collector, and cannot be dismantled for internal cleaning. Pilot Blue-Black has somewhat similar properties to the Sei Boku, but to a lesser degree - it has a nice lubricated feel, but is a tad less velvety and cushioned-feeling than Sei Boku. It is water-resistant, but not fully waterproof. It shades and has some red sheen, but neither characteristic is as pronounced as Sei Boku.
The 51/Pilot Blue Black combination is my favorite only in situations when I anticipate frequent long pauses while writing. In all other situations, the first combination (Pilot #5 soft medium/Sei Boku) prevails.
The Pilot Blue Black does seem to have some oily thickness to it that makes my 51s write smoother as well. It's a great ink for vintage pens if you clean them regularly!
Interestingly, I have been told that since I like the Pilot soft mediums, I might like the nibs on the vintage Parker UK Duofolds, as they tend to be similarly wet and soft. I have yet to follow up on that recommendation, but it's something I definitely intend to try sometime.
Yes, you definitely should get a UK Parker Duofold (the slimfold and junior models can be had for great prices and seem to be everywhere). I have 2 UK Duofold Juniors and both are soft like you describe. My OB nib Junior is especially soft and lovely, but all mine came too try at first and I needed to open the tines a little to get good flow. You might also like the UK Parker 45s, they generally seem to have more feedback than the 51s and duofolds I've tried and also have really soft nibs if they are the UK 45s.