Wow you are asking a lot, a grill and smoker.
So that makes it charcoal, since you need both high heat a low.
The model you showed is economical, but very limited in size.
I would recommend the 22" Weber Kettle, get cheap model with no extras, it is about $80, you can even find deals on Craigslist. You will need some extras to smoke.
• First is the grill with hinged cooking grate, this makes it easy to add charcoal on long smokes.
• Some people swear by the Smokenator
which looks like it would do an excellent job of turning your kettle into a smoker.
Or you can make your own divider, the idea is to get all the briquettes on one side and be able to add more briquettes through the hinged grate. Here was my home made solution
using a old baking tray.
• Charcoal baskets, there are cheaper little rails that keep the briquettes on each side. These are really important for indirect grilling, which is where the weber really shines.
• Some corks, I insert one cork in the lid's exhaust holes which I drilled a hole through and insert a thermometer with 5" stem, or to run remote probe through. This way I didn't have to drill a hole in lid for the thermometer. The cork will burn so you will only get a few uses before replacement, a bag only cost about $1.00.
Lots of tin foil, and you are set, there are other accessories that would help but this will get her started. There are a lot of people on this forum that have started their smoking experience with the Weber kettle. The major draw back is regulating the heat, but there are methods that can be learned by reading the posts on SMF that will help turn out great tasting smoked Q.
The Least Expensive Kettle with no extras
Hinged Grate & Charcoal basket
My home made smoking briquette and heat seperator