Chau, I don't know where you got that second recipe from, but it's got epic fail written all over it. 4T of flour, 1 C. of cream and 3/4 C. parm will give you porridge.
As far as the first recipe goes... people can and do put anything they want in alfredo, but, imo, garlic is a little out of place. Canned alfredo, as has been discussed, is an abomination, but frozen alfredo (Michelina's, Stouffer's) is one of those few times where big business has gotten their hands on a beloved Italian American food and not ruined it. Also, because so many people grew up on frozen alfredo, it has come, to an extent, to define the sauce within America's borders- and frozen alfredo contains no garlic. I can live without the frozen overcooked pasta, but, sauce wise, I have found most frozen versions to be pretty close in quality to the restaurant alfredos I've eaten. In fact, in some ways, the frozen version is superior/more flavorful because it's starch thickened rather than cream thickened. Cream is notorious for coating the palette and masking flavors.
You may want to get into starch/flour thickened alfredo down the line, but to start, I'd go the easier half and half route.
I looked around a bit, and this looks like a winner.http://www.foodnetwork.com/recipes/rachael-ray/fettuccine-allalfredo-con-prosciutto-di-parma-recipe/index.html
The only thing I'd modify is the nutmeg. Nutmeg is a critical component, imo, but the amount here is insane. For this much sauce you want about half a smidgeon nutmeg (1/64 t.).
I frequently add cooked bacon to my alfredo and I can tell you, it's magnificent, so, I have no doubt the prosciutto will be equally as wonderful, but for now, to experience classic alfredo in all it's glory, just omit the prosciutto.
Oh, and omit the salt, the parm will have loads of salt. These chain smoking celebrity chefs with scorched, flavor receptor damaged tongues just don't know when to stop adding salt.
1 (12 ounce) package egg fettuccine
2 tablespoons butter
1 to 1 1/4 cups half-and-half
1 cup (3 healthy handfuls) grated Parmigiano-Reggiano
1/64 t. nutmeg
Lots of coarse ground pepper (you should see plenty of black specs).
should work. Oh, and, the first time you make this, weigh the parm and write it down so you can tweak based on weight rather than volume. Measuring grated parm by volume is a joke.