minimal pipeline and filtering

You should get pretty far simply by marking duplicates. You may not need to do this if you didn't use PCR amplification in your library preparation, but it shouldn't hurt.

Brad Chapman has worked up a "minimal" pipeline, and he shows that it works basically as well as the much more compute-intensive GATK best-practices http://bcbio.wordpress.com/2013/10/21/updated-comparison-of-variant-detection-methods-ensemble-freebayes-and-minimal-bam-preparation-pipelines/.

He's filtering using DP and QUAL. See the comments in the post and referenced code for examples. In my experience, these should be sufficient. However, if you have some sense of what's true and false from an orthogonal method, you may get better results with a careful tuning of parameters. The allele balance (reported under AB) and strand bias counts (SRF, SRR, SAF, SAR) and bias estimate (SAP) can be used as well, as they are strongly correlated with certain classes of error.

The QUAL estimate provides the phred-scaled probability that the locus is not polymorphic provided the data and the model. This is reasonably-well calibrated, so you can specify that you want things where we expect error rates of no more than 1/100 (QUAL > 20) or 1/1000 (QUAL > 30).

trimming

I would be cautious about aggressively trimming low-quality bases from the ends of the reads. Provided the base quality values represent likely errors, you should do just as well leaving them in the analysis.

Moreover, detecting variants on haplotypes resolves many of the problems with using these lower-quality regions of the reads. Although true sequence variants cluster, errors cluster even more strongly. You can see this if you compare the variance to mean ratio (VMR) of distances between true variants (e.g. 1000G variants) to the distribution of distances of any mismatch between the reference and reads in a set of reads.

Errors being somewhat independent, we should expect that the error-ful ends of reads will generate haplotype observations that do not recur and thus rarely propagate up to the level of detection. We can observe this effect here: http://clavius.bc.edu/~erik/freebayes/figures/indel_error.png. In this figure, we've run the same 191 1000G samples with different --haplotype-length settings for freebayes, and measured the indel length-frequency spectrum to observe the rate of a particular 1bp insertion artifact caused by bubbles in flowcells during the Illumina sequencing process. At smaller window sizes, the chance of recurrence of this artifact in multiple reads is high enough that we detect more 1bp insertions than deletions (we expect slightly fewer given results from de novo assembly). As we increase the window size, the artifacts cluster with nearby errors, generating unique haplotype observations. This improves the signal-to-noise ratio.

In summary, I wouldn't trim unless you observe serious problems with the last cycles in your run, and these generate lots of false calls.

removing low-quality reads and bases

Again, I wouldn't remove reads with low mapping quality, or observations with "low" base quality unless you observe very strong systematic problems with your sequencing data. The basic idea is that the method benefits from additional information. Even low-quality information is helpful.

In the pipelines I'm running now, for Illumina data I typically provide the following to freebayes:

--min-base-quality 3
--min-mapping-quality 1

This is because (as I understand) base qualities below 3 act as flags rather than true qualities. Also, mapping quality 0 may mean "multiply mapped." I noticed these settings helped our results slightly.

caveats

Your specific experiment may require high sensitivity or high specificity. To that extent, you should choose appropriate filter settings based on your understanding of the problem. Hopefully this helps shed some light on your options.

When mapping paired-end data to a genome, would anyone consider only mapping one read if the paired mate as well maps? In other words, Read/1 can only map if Read/2 also maps within the required distance?