Economics does get rather maths heavy towards third year, but doing economics in first year requires only a very very basic understanding of maths, no methods techniques are used at all in first year. where you might struggle a bit is with the compulsory quantitative subjects, QM1/QM2/econometrics. Having not as yet touched theses subjects myself i can't comment on them but many people have seem to struggled with it, it's very statistics heavy.
So essentially, do first year eco, you will be fine, do the maths subjects at the same time and see how you go.
In terms of competition that you mention quite a few times, for eco you are in the same classes as commerce students, it's all the same subject, however more broadly you need to stop thinking about 'competiton' it's less a case of 'competing' with each other, because in uni you get a score and it reflects your mark, as opposed to VCE where you score represents your ranking. If you get 90% on an exam, your mark is 90% (ignoring moderation if the exam is too hard/too easy in whihc case everyone gets moved) as opposed to in vce where if you get 90% but everyone else gets 95% you could get a low study score because it's a ranking.
As for the other issues with subjects, just try it all out in first year and pick what you enjoy-i know it's been said a million times- but it's really true, don't pick something because you think it's more related to law.
Finally in terms of study, if you're that keen on doing well follow the 2 hours at home for every contact hour rule of thumb and you should be set for a decent mark.