I'd agree with much of the above by nooby
It's very, very rare I'll buy a single option; unless it's part of some larger Option Strategy (A Jade Lizard, IC's, Spreads, etc). Though I would buy them as part of BUYING a cheap IV credit spread if IV is really depressed. But generally, if it's not one of those situations? The math says I shouldn't be buying them.
But if I were to buy one directionally (I think the last time was at some point in 2018)? I buy as Deep ITM as it makes sense from a Capital Allocation standpoint, and a little bit out in time.
My reasoning is this ...
The higher your Δ (Deep in the money calls and puts)? By definition, that means that when the stock moves, your option also moves in a similar value for $'s. The lower your Δ (Out of the money options)... the stock can move in your preferred direction? But you will not be making the same $ value, unless you time it PERFECTLY so as to get a simultaneous γ explosion.
So if the stock is at $10.00
And there are $20 calls, but the Δ is only 0.10? Your option will only gain $0.10 for every $1.00 in stock movement (not accounting for γ movements). This is why people cry "The Option market is fixed? I bought a $20.00 call, and it went in my direction, but I didn't make any money!! It's a scam!"
No, they bought a sucker bet, and didn't get a gamma explosion at the same time, and they didn't understand the math of what they were doing.
Basically, people are lured into buying what they think are "cheap" options, because they are only 0.05, but they don't really know what they are doing.
Conversely ... if the stock is at $10.00?
And there are $5 Calls, and the Δ is 0.90? Then the option will gain $0.90 for every $1.00 of stock movement (not accounting for γ movements)
This is why it makes more sense, mathematically ... to buy more expensive options, because in the long run ... they're more math advantageous to what you are trying to do.
That's Delta ( Δ ) in a nutshell, and why if you are going directionally? And buying? You want those Δ numbers as high as possible.