Maverick,
Welcome. I am one of the least seasoned or knowledgeable people you will find here, but your situation sounds similar to mine so, for what it is worth, I will share my experience.
I have built a system with the final word always being budget. When I started I had listening room about the same dimensions as yours that was also living room, dining room, and kitchen overflow. I decided on the B&W 602 S2 with a matching sub and never regretted it. I listen mostly to jazz and r&B, some acoustic rock. I found them clear, able to handle being pushed with some occasional hip-hop, and tending toward the warm side. I had stands to place them at the proper height.
I also run an Arcam amp, the AVR200 integrated. It has 80 wpc, and can be adjusted based on your speaker set up: small or large fronts, a sub or not, etc. I have found it to be more than adequate for my listening level (also constrained by wife and kids). The Arcams tend to have more power than they indicate and also to control it well enough that they push well into the upper volumes without getting distorted. You are right, they are not punchy, but I have found mine keeps up very well with Elvin Jones and Chucho Valdez.
My turntable is a Music Hall MMF 7. I now also have an Arcam FMJ23 cdp.
When my first kid came along I decided safest for all to get rid of the monitors on stands and went with Meadowlark Ospreys. They have taken a while to break in, and I had forgotten to reset my amp (large fronts, no sub) but now everything is coming together.
I love the sound of each components. I did not have time or budget to audition extensively, and I barely have the listening time to justify time auditioning. Everything except the AVR200 came used from here at the 'Gon. I trust it far more than eBay. I did lots of reading here and read lots of outside reviews. The people here were more helpful to me; I need layman's terms and trust listener-consumers more than professional reviewers.
From what you posted I would suggest a few things. For speakers, if you can find a pair of the 602S2's, GRAB THEM. Then get yourself a sub when opportunity and $ permit. You will generally get better sound for less money with a monitor-sub arrangement from what I have seen and heard. The floorstanders that are a step up in performance tend also to be a step up in price. That said, I have been so happy with the Meadowlarks that I think you could do well also by picking up a pair of Kestrel II's or Shearwaters. Spendors are supposed to be great for jazz. I looked and looked, but could not find what I wanted. My other serious option was the VonSchweikert VR2, but that would be more $$ than you're aiming for right now.
I'm not familiar with your cdp. What to do with that sort of depends on the ratio of your music, vinyl to CD. Keep in mind that what you start with -- TT, cdp, etc -- is the most you'll end up with. Your amp or speakers will not give you more than the source component. There is lots of talk here about giant killers; wade through it and there is some good info (including as I recall recommendations re: a Nintendo game system).
Also, it seems like you may be well suited for some room treatments. Find a southwest print rug to cover the tile floor, try some curtains on the windows, etc.
Finally, make sure that your guide is how much you enjoy your listening, not what someone else says about the hardware. That way, no matter how much you spend, you can be assured you'll get maximum return on your investment.
Good luck and good listening.