wallet vs keys ?

Money in wallet = buy games on sale = sell for keys = more keys than you could buy initially with same money = prophet.

I think. Not sure though. Maybe I forgot the ??? step.

if you want to trade them for profits and if you are on a region locks free definitely wallet but if you are on a region with locks and want region free gift copies keys would be indeed better (and more expensive)

Why no both.

trading or owning, doesnt really matter nowadays, unfortunately wallet is your answer

I'd say both. Wallet helps with any games you cant seem to trade for keys (as well as region locked games) and well, buying a game from someone in a different country for keys can often lead to it being much cheaper on your part. Why not put all your money into wallet and then buy keys when needed via there, works on both parts.

If you want to own those games, keep your wallet money and don't buy keys.
You won't be able to sell the keys for the same price as you bought them for due to the tax on the community market.
You can always buy keys when you want to trade them for something.

It depends, what's your region ?

keys for me. i'm in a region-locked country without any kind of discounts (thanks valve/publishers/whatever), so it's always a better option to trade with mexican or brazilian people (at 60-70% price).

Buy keys outside of steam for under $2 each, then sell them on the market for wallet funds it's the way to go if you ask me, this way you pay 10-20% less then it's store price + no need to trade for it (which isn't really a thing anymore anyway except for some rare instances like pricing errors and the occasional game in EU2 that's a lot cheaper.)
Only thing you have to keep in mind is that it's best to sell them some time before the sale since prices for keys on the market tend to fluctuate a lot during sales.