what are the verbs that are usually followed by gerund, by 'to' infinitive, by both?

Answer 1

There's a nice list in Betty Azar's Grammar book, as well as in a book named Focus on Grammar. I have neither in front of me, so here's one online:
http://esl.lbcc.cc.ca.us/eesllessons/gerundinf/gerundinf.htm