In MY opinion, the best headphones can detect the diffenece between a whole range of audio components.

Besides measurements of course!

The first point is already the signal to noise ratio as measured at the line output of the laptop.
Becasue there is no galvanic isolation between the laptop power supply ground and the line output ground, inevitably there is too much spurious noise there.

And it gets dramatically worse, as soon as you connect not a headphone ( which is electrically isolated), but an amplifier which is connected to the mains supply. Now we get all sorts of ground loops.

(Ooh...BTW: headphones like a dedicated amp, and not the kind of output that the onboard sound can give; it simply lacs the  high quality OPAMPS and power supply lines that are needed for a proper drive).

The external audio interfaces have symmetrical outputs, which match with the symmetrical inputs of the powered monitors. This also gives you a totally disturbance-free transmission between those components.

It is really toal nonsense, and therefore not done in the professional audio world, to connect a asymmetrical line output form a laptop directly to a monitor. It is also very unwise because the line levels are totally different, and you do not get proper power output.

Well, this was only the first reason of difference.......

Most of us can hear difference between onboard audio and a dedicated outboard unit.

You confused words "most" and "some"

Caravan moves at the speed of the slowest camel. I guess the slowest camel in the chain pianoteq-soundcard-headphones/monitors is the headphones/monitors.

Most of us can hear difference between onboard audio and a dedicated outboard unit.

Indeed I agree with open air; try to compare the Audio Technika with AKG k701 ( of course the3 latter is more expensive).
I have the AKG K550 ( closed) for organ playing, because it has somewhat more bass, but for piano I dislike it. I use the Sennheiser HD595 for piano.

5inch is enough for a small room. With a good brand of monitor speakers, you will not hear any difference between de 5 inch and the 6 or 8 inch models, as they all have similar, flat responses and low colouring.
The main diffenece is the available sound power, and of course extended bass range.

When on a budget, one wouldstart with M-Audio BX5 ( not the newer Carbon, as it is more expensive), like the ones that Phil Best is using https://www.youtube.com/watch?v=mF9xh5YHW8w
And if not enough low end, you can always add a small sub later.

Would an external USB Audio Interface be better?  If so any recommendations?
What would you recommend for Monitors/Headphones?
If I had a dedicated PC for PianoTek, what sort of minimum specs would I need?
Any settings that I should set on PianoTek stage?

I have very cheap laptop (with Pentium 2020M CPU), Audio-Technica TAD400 headphones, USB-MIDI converter (Creative xmidi 1x1)*, no external soundcard. It works perfectly!

I set-up ASIO4ALL, 4ms latency and optimistic polyphony setting. CPU loading is very very low. Sounds perfect. Really, Pianoteq currently is the category killer: for my ears it sounds better than all sampled/hybrid software pianos I tried. "Stage" costs not so much to have almost real Steinway D in your room. Bluthner even better, but for additional price (I wanted to buy it, but suddenly Russian ruble fell by half). It's really good (in contrast to the most software pianos) that you can test Pianoteq without buy it, you just lose several keys.

I highly recommend use open-air headphones. Headhones are always much better than monitors in the same price category. Open-air type feels like as if you have no headphones on your head at all.

P.S. Pianoteq, not PianoTek.

_______
* First I bought chinese 4$ converter, but it doesn't work with sustain pedal: instead of send controller 64 it send note 64 (E4). Surely, you need no USB-MIDI converter at all if your digital piano have USB.

I really don't think I can justify upgrading as the P95 is easily good enough for my abilities but I do want improved sound.  I think I could achieve this by purchasing PianoTek Stage.  What I don't know is what the best way to get something setup without complexity but offers the best value for money.  Also, I don't wish to do mixes, record or perform only play the piano privately.

I already own a Midi to USB lead and this works fine with the PianoTek demo.  I have tried this with my laptop using ASIO4All and the latency is acceptable, however what would be the right way to do this? 

Would an external USB Audio Interface be better?  If so any recommendations?
What would you recommend for Monitors/Headphones?
Does anybody use USB Monitors? 
I have a tiny room, will 5 inch be OK or will I be better getting bigger? 
If I had a dedicated PC for PianoTek, what sort of minimum specs would I need?
Any settings that I should set on PianoTek stage?

This is all very new to me and don't know where to begin so any help would be appreciated.