GTDB works well with QIIME 2, the files are already in an appropriate format (though I’ve noticed the reads are in mixed orientations so best results are obtained when using
extract-reads prior to training your classifier, since this fixes read orientation). I have been using that database a lot recently and would recommend it, but you should be aware that many of the taxonomies used in there are not recognized names (see the GTDB website and paper for more details on this).
This is mostly because SILVA is more recently and regularly updated than greengenes, but many people do still use the latter because it has its own advantages.
As for which database is best, they all have their own strengths and weaknesses. You should just be consistent in what you use if you plan to compare across studies, and you can see the references for each of these databases to evaluate what best fits your biological question.