QWERTY keyboard is one that has individual keys for the different letters (so no need to hit '2' key 3 times to get letter C).
Kerry's recent thread is here but originally she asked about a suitable mobile the Christmas section
Since you know your existing phone works on Vodafone, then you may be able to get an upgrade deal (so you buy a new phone with the intention of using existing SIM in it, avoiding the 10 or 20 quid top-up fee they impose on most new phone purchases - or visit Asda Living where they don't usualy impose that extra!)
As far as using wi-fi at home, which GSMarena shows as "WLAN" (wireless LAN, LAN meaning local area network, ie your home wireless network setup), there are far fewer phones than will do the other things.
What budget did you have in mind ? I just checked a few phones for wi-fi and these seem to have what you want (did not look at more expensive models however):
e2save 110 3MP LG GT540 Optimus
e2save 100 2MP Samsung Galaxy Europa
C.P.W. 100 5MP Samsung S5560
C.P.W.. 90 2MP Alcatel OT 980
e2save. 80 2MP Nokia C3-00
In the list above, C.P.W. is Carphone Warehouse, e2save is e2save.com (owned by Carphone Warehouse)
Then there is the price (rounded up form 109.99 style) and camera MegaPixel spec (2 is OK, 3 is better, 5+ is even better, most will take video clips too, of course).
All the above are working on Vodafone and offer Wi-Fi access at home. There are probably many more!
Suspect, you, like me, hate paying rip-off price for making calls. Vodafone PAYG is 20p/min and 10p per text but an Asda SIM will work (they use the Vodafone network) so you could move your number to Asda (or just get a new SIM, hint: ask for a 5 quid top-up Voucher and you get the SIM pack free) and put that in after buying the phone on the cheap as an upgrade at Carphone Warehouse (as you already have a Vodafone SIM in your text/talk old mobile).
You would need to check Asda's data charges against those of Vodafone to see your internet and e-mail use won't be rip-off, however.