You can connect one of the monitors to the VGA port but it will be noticeably (at least to me) different from the ones on digital connections. It will still work, but the monitor on the VGA connector will be blurry and the colours/alignment may be marginally off. If you don't notice it, you're probably not as picky as I am. And once you add the second card you will be fine (if your motherboard supports it).
BTW Windows is absolutely fine if you use both onboard and an add-in card. Desktops can be be spanned across multiple displays on multiple cards since the introduction of AGP, over twelve years ago. If your motherboard has the right connectors and cables, you are good to go with just one card if you don't game.
You will need to look at the connectors very carefully. Most entry-level monitors will have either HDMI or DVI, sometimes only one of the connections along with VGA. Most graphic cards will have three connectors with a very good chance of one being VGA. Some will add a Displayport connector, and if your monitor doesn't have one you're down to one usable digital connection.
Solution is a card with three directly usable connections. Here is a model on Flipkart with two DVI and one HDMI.
Gigabyte NVIDIA GeForce GTX 650 2 GB GDDR5 GV-N650OC-2GI Graphics Card - Gigabyte: Flipkart.com
You also have the option of using cables and adapters to get the right connections. Electrically (at least as far as this project is concerned), DVI and HDMI are interchangeable if you have the correct cables. Normally, a DVI-HDMI cable or two will be all that you will need to get a bunch of hardware working together.
Re monitors, here is a very crappy one:
BenQ 20 inch LCD - G2025HDA Monitor: Flipkart.com Don't get carried away by LED lighting. It is not a great feature at all. 'LED' monitors only have edge-lit panels, the main backlight is still CCFL. First priority is the panel type. Cheap TN panels will be worthless once you don't look at them head-on. Second priority is the bezel thickness, this is critical in a multimonitor setup. Here is one that *might* work for you:
LG 23 inch LED - E2351VR Monitor: Flipkart.com. My favorite recommendation is from the DEll U series:
LG 23 inch LED - E2351VR Monitor: Flipkart.com OR
Dell 24 inch LED - U2412 Monitor: Flipkart.com
Your budget though, is shot to hell..
And while we're on topic,
http://www.techenclave.com/sell-trade-products/doublesight-triple-monitor-flex-stand-143331/