That's an awfully good car. I usually don't have anywhere near good data like that. But it helps answer some questions you have. My take on your questions below, but veterans on the board might be able to give more competent advice.
You can sell your puts whenever you want, so you would want to choose the expiry that benefits the most from the drop in stock price, not the one that might benefit someone who wants to buy SPY. That said...
I would start from the amount of money that I am willing to risk on this bet. Like you say, options have a wide range of prices, depending on various factors and strike is one of them. Let's say you had $10,000 to make the most of this information you have.
Because you know exactly when the market will start crashing Aug 1st, then you want to buy those puts on Jul 31st. Buying prior to that date means you're buying additional time value in those puts. You don't need it if you are certain when it'll crash. Obviously, reality is much different than that and we're willing for that time value of options in case things don't pan out like we thought they would. Nothing worse than being right about direction of a stock, but being wrong about timing (have the market crash after your puts expire).
With said $10,000 which are available to buy puts to hedge a portfolio or simply make a speculative bet, like you said you could buy ATM, OTM puts with different strikes. I'm sure there are calculators out there which could provide you with excellent PnL simulations for different scenarios, but roughly you could get one of the below:
60 puts, Aug. 21, 180 strike - $1.64
5 puts, Aug. 21, 280 strike - $19.46
43 puts, Sep 18, 180 strike - $2.29
4 puts, Sep 18, 280 strike - $22.10
Obviously 60 puts are better than 4. They give you optionality over 6,000 shares of SPY or $1,680,000 in underlying position. In contrast, for the 4 puts you have only $112,000 in underlying stock. Obviously, a 35% fall in the underlying stock won't equate to you gaining 35% on the $1,680,000 or on the $112,000. That's because different strikes have different deltas, which will indicate the degree to which the option price will move with shifts in the price of the underlying.
- Delta will be around 0.5 on strikes closest to the current price of the underlying and will get smaller and smaller the further OTM your strike is.
- Delta will be the same (around 0.5) on strikes closest to underlying spot, but on strikes which are deep OTM or ITM, (using the same strike e.g. 180) delta will be higher on the longer maturity.
- Delta is dynamic, so it'll increase when underlying price shifts in the direction that makes your trade profitable (down for puts, up for calls)
To put all of the above in practice, again taking your strikes, you have a delta of roughly -0.5 for the two puts with strike at 280 (Aug and Sep), a delta of -0.044 for the Aug 180 put and a delta of -0.055 for the Sep 180 put. As a result, every 1 point downward move in SPY will impact the 4 different potential positions (all worth close to $10,000) as follows:
Aug 21, 180 strike: 0.044 * 60 * 280 = $739.20
Aug 21, 280 strike: 0.5 * 5 * 280 = $700
Sep 18, 180 strike: 0.055 * 43 * 280 = $662.20
Sep 18, 280 strike: 0.5 * 4 * 280 = $560
Differences are not huge. However as delta is dynamic, the above is true for the first point move in SPY. Should you see a large downward move in your favor, the additional gains that you make start to look much different. This is because if SPY moves to let's say 230, then the new deltas for the puts will be roughly -0.166 for Aug 180 puts, -0.92 for Aug 280 puts, -0.186 for Sep 180 puts and -0.89 for Sep 280 puts. Which means that the next point move down (from 230 to 229) will see the below gains in your positions:
Aug 21, 180 strike: 0.166 * 60 * 230 = $2,290.80
Aug 21, 280 strike: 0.92 * 5 * 230 = $1,058
Sep 18, 180 strike: 0.186 * 43 * 230 = $1,839.54
Sep 18, 280 strike: 0.89 * 4 * 230 = $818.8
As can be seen, though initially the value of your positions and initial gains are the same across maturities and different strikes (by design), by the time this reached bottom (180 in your scenario), the Aug 180 puts will be worth roughly $275,000, Aug 280 worth $50,000, Sep 180 worth $110,000 and Sep 280 worth $42,000. Roughly because, as @Yowster notes above, option prices will increase also due to volatility increase.
If you had a car that let you know exactly when the market crashes, you take the risk out of the equation, so you don't care about time decay and other variables, which in reality make or break a trade. In that case you can fine tune that with different combos where you become even more leveraged and increase your gains. But in reality, that's something with a negligible chance of being a successful trade.
BTW what's that stock? My message box is open haha
Later edit: calculations imply the move in a very short period of time. You did give Aug 20th as the day for a bottom, so then @Kim's numbers make more sense for the Aug expiry. Puts expiring in September will more likely have a higher value and percentage gain due high volatility around that time. You can, of course, sell the Sep puts on Aug 21st.