I did it when my Dad was alive and before my one friend went back home. Dad caught the tradition during the war but I think he and I were the only two in the family to really celebrate; it was a sort of bonding thing for us I think.
My wife is from Vietnam, so we celebrate Tet every year. Not nearly as big as they do in Vietnam, but we go to temple for the dragon/lion dance, then have dinner with the family the second day, then eat our with the family the third day.
We give the kids red envelopes with money.
FWIW, Chinese New Year is the appropriate time to wear it. You don’t wear clothes like that at New Year just to “look Chinese”, or to “connect with your history”. You wear stuff like that for Good Luck in the New Year.
Those of you who want to connect with an authentic oriental tradition without feeling uncomfortable about it: Clean the house before the new year and wear good new clothes on the day. This will actually make your FOTB acquaintances feel more comfortable: who wants to hang out with people who are courting bad luck?
Yes, my partner is Vietnamese, and we don’t do too much, but we do clean up beforehand, and go over to his extended family’s for a big traditional dinner. The kids are all given red envelopes and they also play a traditional gambling dice game. On the day of the new year, we sometimes go to see a dragon dance and firecrackers celebration. The kids used to dress up in traditional outfits when they were little. The big tradition everyone concentrates on is to act positive and nice and avoid negative behaviors and activities during the first days of the new year, to “set the right tone.”