Best cost effective lighting for 45 square ft room and how many plants recommended to grow

HID, LEC, LED, CMH?

What's your budget?

Sounds like you have already decided on LED...? If that's the case you want full spectrum not dual spectrum.

If you want plug and play, Gavita or Fluence are the winners for LEDs.

If you want to build some LEDs, someone else will come along and fill you in.

Today's Forcast... Partly Cloudy With A Chance Of Amber.

 

The recommended LED light power is about 28 watts per sq ft.
Power = (45 sq ft)*(28 watts/sq ft) = 1260 watts

There have been some recent complaints about their customer service, but 2 of these would work well:
520w REDSPEC DEEP-RED Dimmable Niemi LED Grow Light Powered With Samsung LM301H & OSRAM 660NM Diodes - Niemi LED

Cheaper, fake versions that have gotten good reviews are available from china. Two of these cost about the same, and are 160 watts more powerful:
Free Pre-wired High Power 600w Samsung Lm301h Mix Red Cree 660nm Hlg Grow Light Full Spectrum For Hydroponic Plant - Buy Lm301h,Samsung Lm301h,Hlg Grow Light Product on Alibaba.com