I'm having a hard time choosing between "à" and "de" before a verb. I've seen "Je serais heureux de continuer" and "Je serais heureux à continuer", and I don't know if they're both correct, one is incorrect, or they have different meanings.
Basically "à" can be seen as the English equivalent for "to". At the same time "de" is used with certain verbs e.g. avoir besoin de (to need), envie de (to want)...actually more in the sense of "for" generally. When both à and de are used in a sentence, à comes before the first verb and "de" before the second one.
But try to see the different usage here: http://www.cnrtl.fr/definition/
Also these questions might be relevant
I'll edit my answer as I find some examples.
I am a french native speaker and it is "je serais heureux de continuer". If you don't believe me just do a Google search with "je serais heureux à continuer" and you'll find only your question.