My biggest piece of advice is to just ride it out until you're feeling better. I had horrid hyperemesis during my second pregnancy and we spent way, way more than normal. I think our grocery spending went down, because I basically didn't eat. However our heating bill went way up, because I spent so much more time home in bed and being cold made the nausea worse. We also spent a ton on the prescription cocktail it took to keep me out of the hospital.
If your biggest problem is that you don't want to eat what the rest of the family is eating, then don't. Have your DH meal plan and cook for himself and the kids. For yourself, have whatever food sounds least disgusting and don't worry about the fact you're eating something different. Try to get some sort of protein in at every meal. Keeping your blood sugar stable helps keep the nausea down to a dull roar. You may also want to talk to your Dr about getting Diclegis or Zofran to manage the nausea.
In terms of meal planning, ask your DH to choose cold/raw foods. They tend to smell less and are often easier to prepare. If you have grocery delivery available, this is a good time to use it. If your insurance covers prescriptions, but you end up taking OTC meds, ask if you can get a script for them. This lets your insurance absorb some of the cost. I did this with the Zantac I took while pregnant.
If you're taking a prenatal vitamin, stop. Those things make many women sicker.