Zero offset is pretty rare. The TE forged heads all have .1" which is typical of most short irons these days, but the longer irons can range from .15 to .3 or more. It's a bit unusual for the clubs not to increase their amount of offset into the longer irons, but I have no trouble hitting the 3-5 irons in this set. They feel very soft and interact well with the turf, and they are a bit of a tweener iron because they're forgiving enough for a high 20s handicap which I was when I first got them, but I don't launch them too high like other forgiving irons and the look suits my eye for aiming. I could easily ride these irons for a couple more years even if I get better. They also gap nicely and look good in the bag, and are good workhorses for the money.
It's not something to worry about too much but I don't know whether the pro was giving you a general tip on picking good irons or if he thinks you'd benefit from more offset. I'd contact him with the specs if possible just to see what he thinks but those are a very affordable and versatile club.
I also like that the hosel can accept either .370 or .355 tip shafts, since some iron shafts don't come in both sizes. Pretty much any shaft whether it be steel or graphite will be usable with these, so I'd consider your budget and fitting info.
This tool will give you some suggestions on shafts, the 4 number/letter code indicates the flex, (a 4 is about stiff) preference for distance, control, or both (I'd advise either C or B but B will probably include more of the lighter shafts) 1-3 is your preferred trajectory with 1 being low and 3 being high (2 or 1 are probably best unless you struggle to elevate the ball) and finally you should ignore the last digit more or less. It indicates what your miss is, with S indicating a shaft that might help a slicer and H to straighten out a hook. Either H or M are fine for irons as this number seems to be based mainly on torque, which isn't a major concern with irons. The last digit might narrow it down but I wouldn't put too much emphasis on it for irons.
So I'd look at the list of shaft ratings for a ballpark estimate of what fits you, or at least what's aimed at golfers like you. 4B2M or 4B2H are probably your best bets so I'd look over the shafts in these categories for something you might like in terms of price and features.
Finally, Pure grips make a midsize model, and they are awesome (I have them on my irons now). You can blow them on and off with a compressor instead of using tape, which is faster and cleaner by a huge amount. If you don't go the compressor route with the grips then it's pretty much a matter of preference.
As a final thought, if you do go with the TE forged, I'd suggest white ferrules if you're interested. They have the model number 86PI on the site and they look really cool:
Custom irons are great because you can get this kind of stuff. The head's hanging at an odd angle so the heads aren't that short in real life.