external hard drives

I want my wife to be able to edit our pics in Lightroom without taking my laptop, so I'm going to put the pics and catalog on an external hard drive.
Two questions:
1. I take it this will work.
2. Any advice about what is a good (e.g. fast, but also small -- since I'll sometimes want to travel with it) external drive? Both the following seem to do well on Amazon:
http://www.amazon.co.uk/dp/B007UOW81...501_pe_epc_dt2
http://www.amazon.co.uk/dp/B008PABFX...501_pe_epc_dt1
It's not clear to me how to rate the speed of the devices (there's no objective speed rating I take it? or is there)
Thanks for your help
David