@KCalhoun , you must be foreseeing a real market dump if you're looking to go big on puts. If that dump happens you've come to the right place so here's my perspective.
From what I gather, you day trade index, sector, bull, bear, and volatility leveraged ETFs with a directional bias where you open a trade early in the morning then scale in and out throughout the day ending the trades sometime before market close and you do it in front of an audience of newer traders so you have to take in account the pedagogical and entertainment value of what you're doing. And now you want to replicate this experience with SPY options to gain some additional leverage.
That last part is key. I imagine if you could just hit a button and make SPXS a 10x leveraged ETF you'd do that instead. You're not looking to tangle with surprise changes in volatility, the bummer of time decay, or any of the other jazz options force on you, turning one problem—directionality—into multiple problems. You're looking for a quasi delta 1, albeit highly leveraged, trade. Great, hold that thought.
Option premium is made up of two parts, intrinsic and extrinsic value. Intrinsic value is the amount you would receive if you assigned the option and sold the proceeds at market. For a put, however much the strike price is above the spot price of SPY is how much intrinsic value the put has and it does not change until expiration for any reason other than changes in the underlying SPY price. Conversely, extrinsic value is much more speculative in nature and is affected hugely by changes in volatility (IV and vega), where if volatility increases, extrinsic value goes higher and if volatility shrinks extrinsic value will decline in kind. Time decay (theta) chips away at extrinsic value too on an accelerating curve. The longer you hold an option, even if the underlying doesn't move at all, the price will decline due to loss of time value and the closer an option is to expiration the more that loss accelerates. Depending on what you're after, both of these can work for or against you either individually or together.
Circling back to directional bias, you want to minimize the effect of odious changes in extrinsic value on your option and maximize the benefit from inherent directionality of intrinsic value. In doing so, your trade will be more predictable, your option will move in line with changes in the underlying, and being new to the option world the trade will be easier to manage.
Practically speaking, to avoid any nasty surprises I'd suggest a deep in the money option with delta of around 90. Instead of daily expiring I'd lean toward expiration in a week or so. That way, in case you decide to hold overnight, you can do that since expiration is still days away. As mentioned in another post, options only trade during regular hours but if held overnight yours will naturally reflect the difference between yesterday's close and today's open so you get some of the effect of buying in premarket. The downside with deep ITM options, as opposed to ATM or OTM, is if the market moves hard in the direction you predicted, you will have sacrificed some leverage and profit. However that's just about the only downside and you do avoid most of the unpredictability of changes in extrinsic value which is what you want anyway since you're day trading to get in and out at a quick profit.
All that said, I don't make directionally biased day trades with options since not being a delta one product they add unnecessary complexity to an already speculative undertaking. For the most leverage, liquidity, flexibility in shorts and longs, tax advantages, overnight trading, etc. I use futures every time. I understand your situation is different since most of your students trade normal hours and don't have futures accounts but for your personal trading, consider it.
Last note: a rough guide to option leverage is multiply the underlying price by the option's delta then divide by the option's premium. Even with a deep ITM weekly SPY put, delta of -.90 you're talking around 10x and that's with almost no extrinsic value so if you bought it, held the entire week, SPY didn't budge, volatility collapsed, and you did no trade management other than selling on the last day, you'd only lose a few dollars. If you buy at the money or OTM, in the same situation, there is no intrinsic value. In that case, the premium you paid for is entirely extrinsic and you lose it all.
Further note, I didn't bring up gamma. It's important but really starts to show its power around the ATM close to expiration spot. If you take one step deeper into trading options
@KCalhoun , I'd suggest getting familiar with it as well as the other greeks.