Joe, in my experience, each of the networks has better coverage in some areas than others. I use "roaming" with my home carrier when I travel, so my phone usually selects the strongest signal in each area. The phone seems to change carriers depending on where I am.
It would help to know which countries your Mom is going to be travelling? One point to note is that whichever network you choose will have the least expensive rates in the country in which it's issued, however if your Mom travels to other countries then roaming charges will apply. I gather from the networks you listed, that you're focusing on the U.K.?
Be sure to buy a quad-band unlocked Phone, so that you'll have both Euro frequencies (900/1800 Mhz). Note that Orange is a single frequency carrier (1800 MHz) as is T-Mobile, although their 3G phones also have 2100 MHz. For normal voice calls, I doubt you'll be using or would need a 3G model. Note also that Hutchison is a 3G carrier ONLY, and if you're buying a phone on this side of the pond, it might not have the necessary Euro 3G frequency.
If you are in fact referring to the U.K., my preference (based on the experiences of relatives that lived there) would be to consider either Orange or O2. One of my relatives had a lot of trouble with Virgin, so that's not a network I would ever use (Virgin is classed as a "Mobile Virtual Network Operator", as they don't actually have their own network).
It's important to look at the rates of each of the carriers, and also the expected calling pattern of your Mom. That way you'll be able to determine which will be the best network to go with. Each of the U.K. carriers have several PAYG plans with different rates based on time of day, whether calling a wireline or a cell on the same network or a different network, etc. I normally use SMS to keep in touch with family when I'm travelling, as it's fairly cost effective compared to voice calls.
Good luck and hope your Mom has a wonderful holiday!