I'm a student and have attended 2 interviews so far. The first one, I was sitting at the reception area and one of the managers came in and met me. She offered the handshake first. She walked me to a room and there was another manager sitting there. She introduced him by name, I said "nice to meet you" and he just sat there. There was a table between us. I wasn't able to judge if the table was too wide for me to do a proper handshake across the table. I tried to read the managers body language and it seemed as if he was the more serious, strict type (which he was) and it didn't look like he was going to reach out for a handshake, so I took a seat. On my way out, the manager I met first said she will escort me out. I reached out for a handshake with the second manager and he shook my hand (it didn't seem like he wanted too. No enthusiasm, he just sat there, very strict).
In the second interview, I was greeted by a manager while I was at the reception again. The manager reached out for a handshake first. He took me to a room where there was another employee and another manager. They didn't reach out for a handshake immediately but they were sitting there smiling and seemed friendly so I reached out for a handshake. The employee gladly returned the handshake and then I turned to the manager sitting down and reached out for a handshake with him as well. He was somewhat surprised but pleased as well. When leaving, we all got up, I shook the hands of the employee, the first manager and then the second manager (the second manager was actually about to turn around and leave but luckily he saw me reaching out for a handshake and he turned back and shook my hand. Again, he was surprised but pleased).
Nonetheless, is it recommended to meet everyone with a handshake during the start and end of an interview even if they don't offer a handshake first? If there is a table between me and the interviewer, is it recommended that I walk around the table or shake the hand over the table?
Edit: I did these interview's in Toronto, Canada. I'm a male and the people who I was meeting were also male (except for the worker whom I referred to as the 'employee' and the manager who offered the handshake first during the first interview). I was applying to an IT position for both interviews.