I am plumbing a bath in my unfinished basement. The drains are existing but need to plumb the hot and cold water supply. The question is, the house has been plumbed with pex (its a flexible colored pipe - red for hot and blue for cold). Should I use this type of pipe? If so, should I run 3/4" to the shower and 1/2" to the lav and toilet or would 1/2" work for all? Next, there are two types of connections available for the pex piping, a compression couple and a more standard connection with a crimping collar. Which would be better? The compression fittings are much easier and less time consuming to install but I don't want any leaks.

As a DIY, you might buy one coil of 3/4'' and use it for everything. If you are going to go crimp fittings, you would then only need one tool.

Myself, I would be tempted to use compression fittings to adapt to CPVC and use it and PVC.

Pex is tried and true this is what I use everyday I use crimp ring style yes the tools are about 100 a piece however you can use "sharkbites " insteed of buying the tool( with any pex you are going to have to buy a tool) I don't like pvc or cpvc for water I just don't trust it and have had bad experiences with it because it can split and leak... like I said I would use shark bite if all you are plumbing is a bath the you could get away with aobout $120 in fittings .vs. $200+ in fittings and tools and as far as 3/4 and 1/2 I would run a 1/2" trunk line for hot and 3/4 for cold and every fixture gets a 1/2 water supply
general rule of thumb is 2 fixures and under 1/2" can supply 3 or more you will need 3/4"