For my website, I always used blogs that speak about the same topic as mine.

"Without getting banned" so there is only one option you have which is web 2.0 site.

Almost anywhere : social media, forums, blogging websites ....etc

You can post on online forum, Question Answering sites (Quora, Yahoo..) Blog commenting.

I haves some solutions for you. First of all, if you don't want to be banned, then don't take any tool hack. Ok? Get you backlink traditionally and naturally.
I recommend some web 2.0 to you: wordpress, blogger, weebly, jigsy...
Social network is the other good choice: facebook, linkedin, twitter...

The principle here is: don't spam !!!

blog commenting, Social sharing and Forum posting give you back link.

Post Backlinks to Directories Online
 

You have high PR Web Directory sites like DMOZ, Yahoo, and many others. Do an online search for " top web directories ". It is a great way to increase your SEO value.

Cmt on BlogcommentLUV , this is a way to get backlink. cmtLUV is a plugin on WP. If this is halpful, like me @@

You can post backlinks in all the high PR sites to get backlinks. There are two types of backlink website one is no follow and other is do follow. Do follow website backlinks are helpful in ranking the specific keyword in all the major search engine whereas no follow backlinks helps in getting traffic but doesn't contribute in ranking the keywords.

You can do it in
1.Forum posting
2.Blog posting

Is there any rule on this forum to post links to our websites, or can we be banned for doing so?

Regards!!

You should find some forum to set up signature with backlinks

Post your links on Web 2.0