Buy chests, sell chests, buy energy sigs
It must of already been mentioned but the starter pack is pretty good for the expansions. Other than that the chests and reselling is the best option. Don't buy the sigils from the plat store, u get a better deal from players at the auction house. Then just spend the gold from the chests on things that u need only. Well this is what I do anyway and it works well for me
Ok, now that I looked into chests, it's obviously the best option and I really have to agree that sigils are one of the best investments to make as they benefit you forever and solve energy issues.
Just to put it out there, as long as chests sell for the biggest plat/gold ratio, it will always save you money, plat, time, whatever/everything to buy chests, then resell them and use the gold to buy what ever you need. As Romeo said.
Just as an example, if you sell 10 event chests for a total of 300k which goes to 400plat : 300k gold. Now, you spend that gold on sigils at 50k a crate (10 sigils) that's 6 crates which totals up to 480plat. So you just saved yourself 80 plat or 60k gold if you use it to sell chests. So basically you want to watch out, if you sell a chest for 30k and buy a sigil crate for 60k (or just double), you might as well just buy the sigils with plat. I know it's pretty simple I just thought I'd put it up here.
I'm not sure about backpack expansions, but I usually see bank expansions going for 2k each, and you can get better deals, so it doesn't seem worth it to me to get expansions with plat as bank does essentially the same thing if pack is too expensive.