Does it matter which host I use for my light wallet?
No, you can use any host as long as it's in sync. You can check this by going to http://www.iotasupport.com/lightwallet.shtml and matching the milestone with those shown in the #botbox channel on Slack. If the host that you're currently using becomes un-synced with the network, simply switch hosts ("Tools" > "Edit Node Configuration" > choose a different host from the drop down menu). You may need to close and reopen your wallet for the change to take effect.