Personally I'd go with a refurbed business laptop that's a couple of generations old. The main difference is battery life, you won't be getting 8 hours+ like some of the modern laptops but you should get 3 or so. You can plug it into your keyboard, mouse and monitor but it is convenient to have a laptop occasionally.
A lot of them tend to be Dells and Lenovos which are pretty tough (so long as you don't care about cosmetic marks). Going the refurb route gets you much more power for the price.
Personally I like the Lenovo X220 but the Dell Latitude's are perfectly decent as well. There are a few refurb companies on ebay (look for the long established ones with a lot of ratings). I've purchased from this one before with no issues:
This is good value per the specs, but I'm not that familiar with HP
http://www.ebay.co.uk/itm/HP-EliteBook- ... SwB-1Ypy05" onclick="window.open(this.href);return false;
Big screen Dell
http://www.ebay.co.uk/itm/Dell-Precisio ... SwB-1Ynffh" onclick="window.open(this.href);return false;
Decent value specced out with an SSD and additional memory (8GB is the most you'd need)
http://www.ebay.co.uk/itm/Dell-Latitude ... Q#viTabs_0" onclick="window.open(this.href);return false;
Similar but you can upgrade the processor
http://www.ebay.co.uk/itm/FAST-Windows- ... XgS64GzIwA" onclick="window.open(this.href);return false;
Realistically an i5 processor and 8GB of Ram would be more than enough for your needs.