Unfortunately the biggest review I could find of this was from 1988. But the most recent one isn't bad: Geng, Hoff and Umen, 2014, "Evolution of Sexes from an Ancestral Mating-Type Specification Pathway" http://journals.plos.org/plosbiology/article?id=10.1371/journal.pbio.1001904 Sex evolved multiple times.
A lot of the work done on this is pointing towards disease as the original selective pressure for sex. Most of this is done with species that have different sex systems within them, subjecting them to different challenges, and seeing which sex system works best. It's only really in disease challenge scenarios that you need recombination and can overcome the cost of males. For instance, it is actually news that a sexual population of Daphnia pulex - a crustacean that normally clones itself most of the year - was found resilient to invasion by asexual clones, as that almost never happens in the genus.
(Innes and Ginn, "A population of sexual Daphnia pulex resists invasion by asexual clones",
If you are larger, smaller things can invade you and evolve against you quickly; if you're multicellular, this problem increases many-fold. The only way to keep up with parasites with shorter generation times than you is to recombine.
You seem to also be looking for selective pressures on sex systems. One of the best ways to think about this is to examine how different sexual systems evolved in areas of life with diverse ones. See Susanne Renner's "The relative and absolute frequencies of angiosperm sexual systems: dioecy, monoecy, gynodioecy, and an updated online database." American journal of botany [0002-9122] Renner, Susanne yr:2014 vol:101 iss:10 pg:1588 -96 http://www.amjbot.org.ezproxy.is.ed.ac.uk/content/101/10/1588
....because flowers do a lot of different things!
As for sex determination systems, I don't know - but bear in mind founder effects. If your determination system isn't causing big problems there's no huge reason to stop it. Haploid-diploid: it has one obvious advantage - controlling the sex of your offspring by needing one fertilised. But that's a just-so story I just made up.