SCHK
Schwab 1000 Index ETF
stock NYSE ETF

From that list. VOO. I prefer SCHK over VOO as it covers mid caps a bit. Lots of popular ETFs from Schwab but the big K is often overlooked.
VTI is fine too but I don't like total market ETFs. Only because I prefer to exclude small cap GROWTH which historically sucks.
No to SCHG. It makes no sense to me to tilt towards bad PE ratios. Past performance chasing works great until it doesn't.
No to SCHD. It's been doing great YTD but focusing on dividends creates tax drag.

The problem with VTI, in my view, is that it is only 10% small-caps.
Of those small-caps, half of them are small-cap growth, and half of them are small-cap value. Small-cap value has historically outperformed the market. Small-cap growth has historically underperformed the market. So they almost cancel each other out.
AVUV is an ETF that is strictly small-cap value.
So combining VOO + SPMO + AVUV would give you Large-Cap Growth/Value + Small-Cap Value. Which is a pretty diversified US portfolio.
If you wanted to be slightly more diversified and include Mid-Caps, you could replace VOO with SCHX (like VOO, but top 750) or SCHK (top 1000), but it wouldn't matter much I don't think.
As far as moving together, value (AVUV) and momentum (SPMO) tend to move independently of each other. Not all the time obviously. In a big crash, everything might fall, but one or the other will probably rise from the ashes much faster than the other.