The numbers are basically the scale, like the ones you see on maps. 1/144 is the smallest size you can get for mobile suit models, with bigger ones coming as 1/100 and 1/60. To get an idea of how big a model can be, multiply any of these fractions with 20 metres (the average size of a Gundam).
The "grade" basically means the detail put into the kit: how good it looks, how well it moves, and as a result, how hard it is to make. Here are all the grades that matter right now (links lead to a list of all kits of that grade in order of first released).
These are usually available in 1/144 size and average around USD20, are best for beginners. Use the HG Categories link within to get to specific series, though given his likes, you won't find shit he WON'T like here.
1/100 size kits, varying in price, but definitely more than High Grades. Master Grades cover the entire franchise, and hence are not categorized by shows. Best done after practice on some High Grades first.
1/60 size kits, all well over USD150, these are considered the ultimate test in Gunpla building (along with some really hard Master Grades). DEFINITELY not for amateurs to buy or try, unless they have help from someone who knows what he's doing.
The description in the link says it best: "The small size and affordable prices of the High Grade, the advanced inner frame technology of the Master Grade and the massive part count of the Perfect Grade." Can be considered along the same difficulty as Master Grade.
Another general rule of thumb: try to avoid really old kits unless you're an expert in painting, glueing, and making things look good. Older kits tend to look bland when just snap-built (term for building without paint or other aesthetic changes), and have certain weak parts.