Amp + Speakers for a 13 ft X 10 ft room

Tekton M-Lores $699.00
Shuguange S300I - $799.00 (SET amp that uses 300B Tube) No Remote. Its is being closed out and is on sale for a considerable discount. I think they originally sold for $1000.00 You can upgrade to the Shuguange Tube Set upgrade that Granyt Fidelity sells at a later time. You can buy the S300I directly from Shuguange or Grant Fidelity
You didn't mentioned if you wanted a digital or analogue source.
The best source I can think of in your price range is a used Oppo95, they are selling for $800.00 and under (one listed now for $775.00) Since the release of the Oppo 105, the 95's are starting to sell. Before that you didn't see many (any) used for sale.
You can play all CD formatts, and more and more great music is being released on SACD.
Clear Day Speaker cables would be the ones I would look into ($350.00 for shot gun). My Audio Cable Company has a palladium interconnect ($179.00) that I think are hard to beat for the money. I think that adds up to around $2,800.00. Also you may want consider a Primalua Proloug 2 integrated amp (They sell used for $800.00) instead of the S300I, Its a better build then the S300I. The advantage of the Shuguange is the 300B SET circuit would make those M-Lores sing .

Small Dynaudio's(Excite X12's,Audience 42 or 52's)& a Peachtree Audio Nova Integrated Amplifier driven by either computer via USB or any half way decent DVD/CD Player through Toslink is guaranteed to put a smile on your face & stay within budget!

Silverline Minuets are THE bomb in a room that small.

NEver heard Tekton M lore but like the design and approach.

I've been itching to try something high efficiency that are floor standing and larger than my tiny but game Triangle Titus monitors. How can you go wrong at that price? Nice!

The NHT Classic 3 speakers are excellent, and can be found for $400 new. List at $1000. I have a pair in a 11 x10 room and they work great. You could add a Classic 10 or 12 subwoofer for another $350. For an integrated amp with enough power, I would look at the Marantz or Musical fidelity. You can get both with a phono preamp included. for a turntable, I would get used Rega 3 with arm, VPI HW19 or Scout or a TOTL japanese direct drive from the 70s when they cared, especially if you wanted an auto table. Sony PS-x65 or 70 is excellent.