If you dont already have ANY of those tools, that's not a bad way to go- although the price is kinda high in my opinion. I see that it's out of stock at the moment, so perhaps that will give you time to watch your friend and make some decisions based on what you feel your needs are for how far into this you want to go.
You'll want a more expanded screwdriver tip set (hollow ground), far more punches of all different types, far more miniature files (jewelers, gunsmith- fine and medium), various stones of various types and shapes, 8oz and larger ballpeen hammers, channel lock pliers, shotgun magazine cap pliers, calipers (I prefer dial type), ball tip allen wrenches... I could go on, but you get my point, right? I know a guy has to start somewhere, but it really is a lot to do about amassing as you learn.
Some things don't have to be top of the line, but things like punches, files, and stones- hopefully you'll learn that cheap is deffinitely not the best way to go. It took me a long time to work out a piece of Harbor Freight crap punch that broke and lodged itself firmly in my face right below my safety glasses.
Speaking of safety glasses- get some. If you wear Rx glasses, spring for Rx safety glasses and wear them religiously.
Oh and don't buy a dremmel tool. If you have one- hide it where you can't find it for a few years. Anything worth doing is worth doing right by hand. And if you goober up a finish, piece, or part with a dremmel- you'll spend a lot longer fixing that goober up... by hand.
There is never a good reason to get in a hurry and take shortcuts- unless the area where you are working is on fire, then feel free to leave with all the hurry you can muster. Plan each job and each step before you start- get in the habit of making drawings and notes of those jobs/projects and steps. Taking the time to do that will help you mentally envision your steps and progress and help you recognize when you run into an unexpected problem.
And speaking of recognizing unexpected problems... those happen more frequently than you think. You may be presented with a particular malfunction or problem, and your experience or logic may tell you the cause is __________. But once you get into the guts, you may discover something totally different and unexpected. Over all the years of folks making and designing firearms, apparently nobody was put in charge of making sure all the alcoholic and sadistic Engineers stayed out of the drawing rooms. They'll make parts that perform two or three different functions, hide them amongst normal looking parts, and apparently not feel the least bit remorseful about it.
Brownells books "Gunsmith Kinks Vols 1 thru 4" are some great reading and reference materials- I highly recommend those.
I've been working on firearms quite regularly for about 14 years now. I don't and will not call myself a Gunsmith- I respect the one's with the certifications enough to owe them that. I weld and I'm quite good at it, but again for the same reason- I'm not a welder. I humbly ask you to do the same and to give respect, credit, and props to those who truly are the professionals and masters.
I know I made this a long read- sorry. But, I hope you do well and enjoy the hobby. Hope I was able to offer at least a little help and insight.
