I hope the fluttering and flattery works out well
A few things to consider before you go shopping though...
1) Will the monitors be permanently connected to the laptops, or will they be plugged in and removed regularly? That's important because the different types of connection (VGA/DVI/HDMI) have different levels of robustness and resistance to damage when being connected. Although it is subjective, my own view is HDMI is possibly better than VGA and DVI is more vulnerable than both. If the laptop gives you a choice of VGA or HDMI (I agree with jc26red that the usb-like one may be HDMI) then try and use that if you can.
2) Try and keep it as simple as possible - if both the laptop and monitor have VGA connections then use a VGA cable. Adapting or converting from one type of connector to another is opening yourself up for trouble.
3) There is a difference between 'adaptors' and 'convertors' - just to confuse everyone
Adaptors normally just allow one kind of physical connector to be used with a different kind of physical connector, they don't have electronics inside (e.g. VGA to DVI-A). Convertors use electronics to convert one kind of signal into another (e.g. USB to VGA). Applying point 2 above it is best to avoid convertors if at all possible. Adaptors are ok, but straight connections (e.g. VGA-VGA) the best.
4) If you have to use an adaptor or convertor, try to have it on the monitor end. The connectors are not very strong nor designed to be moved around too much, so they are better attached to the non-moving monitor than the laptop that gets moved around on the desk. There's also the risk that an adaptor/convertor plugged into the laptop gets taken away with the laptop and lost.
5) It is worth looking up the different types of connector - VGA, DVI-A, DVI-D, HDMI - on something like wikipedia, just so you have a better idea of what you need. The looking pathetic/flattery option might work, but if you end being sold a £20 convertor with 90% discount you'll still be worse off than buying a £1.50 adaptor which might do the job just as well.
If you can post the make and model of the laptops and monitors we might be able to help you figure out what you need before you head to the shop
Edited to add: The above is based on me spending years looking for a second video card to go in my PC so I could use two (VGA) monitors to make transcribing easier. When I finally gave up the search and looked into the different types of video interface I discovered that a £1.50 adaptor would allow the second VGA monitor to be plugged into the 'spare' DVI-A output on the back of the PC. Cue much slapping of forehead and wishing I'd looked for a simple solution first!
