While Mary and Howard have given good advice ... 2 cents worth here ...
First, Windows 7 ... isn't server ... you might be making reference to the chosen user/workstation operating system. Moodle is a true server application thus best hosted on true server hardware/connectivity.
Second ... while you have provided what you'd like to do with an LMS, consider that getting it up and running is usually 'tip of the iceburg' .... any LMS.
Towards the second ... will you be the 'Moodle Master' ... or primary Admin? Will that role be a 'primary hat' or a 'secondary hat'? Do you have the time that might be required? or will that role be delegated to someone else?
There are several things one might need to ask a provider of whatever you choose ... things like updates/upgrades, backups (that's at 2-3 levels ... server itself ... site ... + courses) ... and, depending upon how the training is to be presented to users (lots of videos? scorms? etc.) the consideration of space/resources. Granted one doesn't know what one doesn't know ... but any online training usually grows (if it takes off/flies) ... that growth needs to be anticipated as much as possible - if possible.
All this to say, it might be well worth your time to 'tinker' some more as investigation might lead to discoveries of things like resources/space/hosting, etc..
LIke I said ... 2 cents worth ...
'spirit of sharing', Ken