I completed my hom through the use of multiple characters, and it worked well. Just keep in mind that you'll have to unlock areas for each character, so you probably want to avoid going to the same place with two characters, because that can be quite timeconsuming after a while (that's what I found out the hard way).
That said I did it using my ele and ranger mostly, as well as my derv and sin. I feel like the easiest was with my ele because I could just very easily run as a AP caller with discord necros through most areas. So if you want to run on several characters you'll have to have more tapestries and you might have to equip more heroes and figure more on your teambuild. The good side with running multiple characters is that for example your faction character have already beaten factions, so you don't have to do that and travel through all of factions again. Plus, at least I, find it more enjoyable to switch characters every now and again.
So if I have to recommend a profession I'd say go with ele, because energy storage synergizes so well with the ap build. But the timeinvestment you've put in your existing characters is also worth a lot.
If you want tips on how to fill your hom you'll need to link the hom page and update us on how much money you have.