Alexander III Lifetime (Newbie Buying Questions)

A little background first. I used to be very into collecting coins. Keeping every Wheat penny I saw and knowing which coins were silver and keeping them as a kid. I'm not a serious collector now (Age 28), but I still have the interest. I'm looking to purchase an Alexander III Lifetime issue coin. I'm aiming for the bigger showy versions. It seems some Tetradrachms (My terminology may be way off due to this being research on this site and google) are the biggest representations at 25-30mm and then Silver and Bronze Drachms are usually 17-20mm or so.

The reason I'm looking to make the purchase, is for my brother's graduation present. He's never been a huge coin guy, but he's a big history buff, especially on warfare. His name is Alex, so I thought it would be cool to get him a coin from the reign of Alexander the Great. I want something that looks cool, so that's the big reason for the preference on size and I'd also like a COA paired with it because I don't know my stuff and that makes for a nice display.

Pricing
Bronze Drachms seem to be $10-100 depending on quality and rarely feature a COA because of the COA cost to coin value. Why authenticate a $30 coin with a $25-100 COA?

Silver Drachms seem to be anywhere from $60 for a bad quality non-COA coin and sky is the limit for COA with nice quality and most seem to be $130-250 for VF and a COA.

Tetradrachms seem pricier and I'm more unsure as to what they are. Are they a higher "denomination" Greek coin?

Any recommendations for my search? I would be ok losing out a bit on taking a lower quality Silver and getting it authenticated myself with a seller that has a guarantee. I know the COA cost sort of kills it if its the same as the coin value, but this is for a gift and the display aspect. I'm hoping to stay under $200. I might spend more if I can get another family member or two to split the cost and go in with me on his gift.

I really like the test cuts as well. I think he'd find that very cool as opposed to a normal coin, even though they're typically valued lower. Maybe there are other special modifications I haven't seen that would also be preferred.

Maybe you could even recommend some other item besides a coin relating back to Alex III that a history buff would appreciate.