I'm starting a new project. I familiar with TortoiseSVN, and all its downsides. Shall I start using Mercurial instead? What are the pros and cons using Mercurial over Subversion?
I enjoyed reading Hg Init: a Mercurial tutorial. It has a chapter called Subversion Re-education which might be worth a read in your situation.
Also there is a Mercurial client called TortoiseHg which is similar to TortoiseSVN. You might want to check out Bitbucket also. I have used it in a couple of school projects and it's pretty cheap and even with the free plan you get one private repository.
The content of Mercurial: The Definitive Guide is available online, for free.