There are a lot of acceptable options available.
The cheapest is the HDPE bucket. Make sure it is food grade quality. They work fine and even some bigger name home brewers use them all the time. Personally, I don't like the way the lids seal (or don't) and dislike taking the whole lid off to see what is going on inside. Personal preference.
Next is the carboys. I do the majority of my brewing in a plastic carboy. I dislike the clumsiness of the glass carboys and the weight when full. These have a smaller bung on top, so there is less of an air exchange when removing them. That said, they are more of a problem with removing bags of hops, oak cubes, fruit, or other materials added during the fermentation.
Some people use sanke kegs for fermenting. Never tried them, so cannot comment.
Conicals are pricey and, at least to me, take up more room than I can afford in my fermentation chamber. Since it is not unusual for me to have 4 to 6 carboys going in the winter time, the space can become tight. The ability to dump trub and collect yeast is, at least on the surface, attractive; it really doesn't seem that much more effort saving than recovering yeast after bottling.
Others may differ in practice, but I have not seen much use in conducting a secondary fermentation. Primary can sit on the yeast for 2 to 3 weeks without issue and the only time I do secondary is when I am doing a large fruit or other fermentable addition (and even then I try not to).
In the end, it comes down to your particular practices and needs. Maybe at a lower price point, the conicals would be more attractive, but right now I just don't see myself getting any added advantage from them. YMMV.