Here is a list of stock-selection criteria that were useful in my point-in-time S&P 500 testing independently and in combinations.

Momentum / relative strength

6-month return
9-month return
12-month return
12-1 momentum: return from about 12 months ago through about 1 month ago
Require longer-term return to be positive
Momentum deterioration test: compare the most recent 9-month return with the two preceding non-overlapping 9-month periods

Moving-average / trend strength

Price > SMA100
Price > SMA200
SMA30 / SMA180 ratio
SMA50 / SMA180 ratio
SMA50 / SMA200 spread, preferably normalized: (SMA50-SMA200)/SMA200
Ranking by strength of the moving-average relationship rather than merely using a yes/no crossover

Position in the long-term price range

PHL: current price divided by a combination of the trailing-period high and low
Test both roughly 252-day and 320-day versions
This was especially useful as a final reranking criterion after another screen had narrowed the universe

Volume / accumulation

Signed AD over about 63 sessions: reward volume on up days and subtract volume on down days
Chaikin-style accumulation over multiple lookbacks
Average dollar volume over about 40 sessions
Average dollar volume over about 200 sessions
Volume criteria were often more useful after a momentum or trend prefilter than over the entire S&P 500

Short-term pullback / anti-chase

Very short-term return, especially around 5 days
Rather than simply buying the biggest short-term losers, try eliminating the strongest recent gainers before applying the next ranking
10- to 12-session return divided by longer-term volatility
Low short-term-return / volatility ratio
These were particularly useful when applied inside an already-strong longer-term candidate pool

Volatility / downside-risk measures

63-day realized volatility
Longer-term geometric standard deviation of daily returns
Downside deviation, including approximately 63- and 84-session versions
Return divided by volatility
Return divided by Ulcer Index
Low-volatility or low-downside-risk reranking among a small set of otherwise attractive stocks

52-week / recovery-type measures

“Escape” measures based on how strongly price has moved away from a prior low
These worked much better when followed by a short-term pullback criterion and then a long-term price-position criterion than as a standalone screen

Price-path / information measures

FIP / information-discreteness measures over roughly 189 sessions