I'll chip in on the ChIP-seq part of it (ho, ho, ho).
I use the background level of enrichment to guide the filter threshold for the average count. There's a number of ways to do this, but the easiest is to cut your genome into large bins, count the number of reads in each bin, calculate the median of the average counts across all bins and then scale that average count based on the ratio of the bin width to your median peak width. This gives you a reasonable indication of what average count you might expect in the absence of binding, assuming most genomic locations are not bound.
There are some more sophisticated strategies using local or control-based background estimates, but I find that a global estimate works pretty well. You can increase the stringency of the filter by asking for all regions that are some X-fold change above the expected background coverage, where a "good" value of X might be 3-5, depending on the strength of enrichment for your protein target (e.g., higher for TFs, lower for histone marks).
Honestly, though, any half-decent peak caller should not be calling peaks in regions that have very low coverage, so I would be surprised if there is any filtering that needs to be done at this stage. In other words, the peak-caller should have implicitly filtered for you (though there are difficult challenges with making this implicit filtering compatible with differential analysis tools like DESeq(2) and edgeR).