If your band is getting too loose it can cause a problem with underarm fat. Basically what happens is that it sneaks because the wires because the band is night tight enough to hold the bra in place so it moves while you move throughout the day. If you want to avoid underarm fat absolutely make sure your band is tight enough.
Also, some brands have higher wires underneath the arms than other. You might want to try Panache or Curvy kate, for instance, because they have wider wires and they come up higher so they'll be more likely to keep that underarm fat in place. Both you can find on ebay for cheap if $$ is an issue (check ebay UK too!!!).
As for styles. I'd say some of it is personal preference but definitely not all of it. Often times women find that different styles are flattering on different breasts. For instances, plunges tends to work better on firmer breasts (because they don't have spillage towards the center), whereas softer breasts without a lot of natural shape do better in more full-fit bras because they prevent the breasts moving around (so that happens A LOT with soft breasts). Certainly, you can try (and own) styles outside of your normal, but typically women find a certain style works best for them.
Just to give you an example. I have extremely soft breasts and a long torso. That means I want bras with a lot of coverage, I also prefer padded bras that give me a lot of uplift (because of my torso length and because my underbust is the smallest part of my waist so bras that sit too low cover that up) and I like wires that come up high (against because of the soft breasts and long torso). So bras that I prefer are the Curvy Kate Thrill Me and Ewa Michalak bras. However, mostly that comes from testing bras a lot (but reading reviews can really cut back on how much you need to test for yourself).
ETA: I hand wash all my bras. Heating/cooling can wear down the elastic much quicker on bras and I really do try to get the longest lifetime out of them as possible. Machine washing can work but it will cut down the lifetime on your bras.
Another bra thing...
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