I tend to wear a block colour dresse with a simple shape, White Stuff or Seasalt usually, with tights and knee lenght leather boots.
If it's cold I add a long cardigan/jacket. I think a plain cardigan, long with no pockets, waterfall or shawl collar, can look reasonably smart, as long as it's the same colour as the dress.
I usually go for black dress and boots - it's a handy work uniform. I have a couple of jackets for smart, but I find it's hard to get one that doesn't add to my roundness, I feel I wear them to indicate that I am in professional mode.
In the summer I sometimes wear wide leg trousers and fittedish top in the same colour, often the tops a PP suggested, the MandS boatneck. I go a size up with the top so it skims rather than clings.
I dress it up with a jacket, dress down with a long waterfall type cardigan, all in the same colour, and wear with loafers.
I'd wear this in the winter too, but just can't find warm, comfortable smart trousers that fit me, like you I'm pretty round, and tights under summer trousers just feels weird.
I wouldn't advise any serious control underwear - too uncomfortable to sit in work all day. A slip will help a dress or skirt and top to skim rather than cling, so lots more comfortable.
Final word of advice - better to be a bit over dressed on your first day than under dressed.
Congrats on getting the job - you've overcome real bias against women, older women and larger women, so you must be excellent!