This is probably more than you wanted to know, but here goes.
There is super-twist nematic (STN) which is the simplest type of Liquid Crystal Display (LCD). STN has slow response times. DSTN (dual STN) was developed by splitting the screen in half to reduce the response time. STN and DSTN are both passive matrix.
Thin-film transistor (TFT) uses more transistors and has a faster response time. Metal-insulator-metal (MIM) uses diodes instead of transistors. TFT and MIM are both active matrix. TFT is superior to MIM, but MIM is cheaper to produce. Toshiba and Seiko-Epson produce some MIM LCDs. I have not checked if that is all they produce.
There are actually three types of TFT displays: amorphous silicon (a-Si), polycrystaline silicon (p-Si), and single crystal silicon (x-Si). a-Si is the most common to the best of my knowledge. I do not know enough about them to give you more information on the subject.
There is also glass plasma screens which are better than LCDs but more expensive.
Now to actually answer your question main question. I would definitely go with TFT (which is a type of active matrix). I would have recommended you look at the Samsung LCDs, they seem to be some of the cheapest and decent for what you pay.
I have not seen the 560v. There is a 570v?
FYI, The 151s is an a-Si TFT AMLCD.
The 151s and the 570v both have the same max resolution, refresh rate, and pixel pitch. The only difference in specs I can find between the two is that the 151s can be viewed from 140 degrees, and the 570v from 120 degrees. I have personally only seen the 570v. I have not seen the 151s.
151s:
Type a-si TFT/TN Size 15" Pixel Pitch 0.297mm Brightness 230cd/m² Contrast Ratio 300:1 Viewing Angle 140º/120º (H/V) Interface Analog
Horizontal Rate 30-61 KHz Vertical Rate 50-75 Hz Maximum Pixel Rate 80 MHz
Dimensions Set (W* H* D) inches 15.4 x 15.1 x 6.8
Weight Net (lbs) 8.8
The 151s has:
Elegant Slim Design, Built-in Power Brick, Touch-installable (bracket supplied free as needed) and Pivot Stand version available
570v:
Type TFT LCD Size 15" Pixel Pitch 0.297mm Brightness 200cd/m² Contrast Ratio 250:1 Viewing Angle 120°/110° (H/V)
Horizontal Rate 30-61 KHz Vertical Rate 50-75 Hz Maximum Pixel Rate 80 MHz
Dimensions Set (W x H x D) 15.2" x 14.4" x 6.6"
Weight Net 12.6 Lbs
The 151s is bigger and lighter, the 570v is smaller and heavier?
They are both about the same price.