The simplest solution to fire-and-forget is to pick something like a Target Date mutual fund made up of low-overhead index funds (within your 401k or a Roth IRA, perhaps) and set up automatic purchase to that. If you're talking about limit orders and so on, that ain't simple.

There is no such thing as buying at the best price.

That only exists in hindsight.

If you could consistently predict the lower bound, then you would have no reason to waste your time investing.

Quit your job and bet with all leverage in.

What if the price never reaches your lower bound and the market keeps rallying?

What if today is crash day and you catch a falling knife?

I'd say the best strategy would be just buy at whatever the market price is the moment your investment money hits your account with the smallest possible commission.

Short answer:

If you can afford the cost and risk of 100 shares of stock, then just sell a put option. If you can only afford a few shares, you can still use the information the options market is trying to give you -- see below.

Why:

A standing limit order to buy a stock is essentially a synthetic short put option position. [1] So deciding on a stock limit order price is the same as valuing an option on that stock. Options (and standing limit orders) are hard to value, and the generally accepted math for doing so -- the Black-Scholes-Merton framework -- is also generally accepted to be wrong, because of black swans.

So rather than calculate a stock buy limit price yourself, it's simpler to just sell a put at the put's own midpoint price, accepting the market's best estimate. Options market makers' whole job (and the purpose of the open market) is price discovery, so it's easier to let them fight it out over what price options should really be trading at. The result of that fight is valuable information -- use it.

Long answer using options:

Sell a 1-month ATM put option every month until you get exercised, after which time you'll own 100 shares of stock, purchased at:

option strike price - total price of all put options you sold until exercise

This will typically give you a much better cost basis (several dollars better) versus buying the stock at spot, and it offloads the valuation math onto the options market. Meanwhile you get to keep the cash from the options premiums as well.

Disclaimer: Markets do make mistakes. You will lose money when the stock drops more than the option market's own estimate.

Long answer using stock:

If you can't afford 100 shares, or for some reason still want to be in the business of creating synthetic options from pure stock limit orders, then you could maybe play around with setting your stock purchase bid price to (approximately):

bid = spot - (spot * iv * sqrt(days/365) * ndev)

spot = current mark price of stock 
iv = implied volatility of front-month ATM option (see options chain)
days = number of days you expect to wait for a fill
ndev = number of standard deviations 

See your statistics book for how to set ndev -- 1 standard deviation gives you a 30% chance of a fill, 2 gives you a 5% chance, etc.

Disclaimer: The above math probably has mistakes; do your own work. It's somewhat invalid anyway, because stock prices don't follow a normal curve, so standard deviations don't really mean a whole lot. This is where market makers earn their keep (or not).

Long answer using stock, take 2:

If you still want to create synthetic options using stock limit orders, you might be able to get the options market to do more of the math for you. Try setting your stock limit order bid equal to something like this:

stock_bid = put_strike 

Where put_strike is the strike price of a put option for the equity you're trading. Which option expiration and strike you use for put_strike depends on your desired time horizon and desired fill probability. To get probability, you can look at the delta for a given option. The relationship between option delta and equity limit order probability of fill is approximately:

probability of fill = abs(delta) * 2

Disclaimer: There may be math errors here. Again, do your own work. Also, while this method assumes option markets provide good estimates, see above disclaimer about the markets making mistakes.

Stevegt has a great answer imo.

I get into stocks with puts (selling).

You can also buy puts at a lower strike or further out in time at the same strike to hedge against massive losses.

Back in the 90's put selling was all the rage...until the market dropped far further than many people could have imagined.