Quote -
Tiff format gave me 502 Kb but no background, it was transparant.

PNG was similar no background

jpg was exported at only 58.2 kb with background.

That depends on your viewer and how it interprets Tiffs and PNG formats. Not all viewers interpret those backgrounds as transparent. Though, in something like photoshop, a transparency for a TIFF or PNG background is standard. Check your file import features and disable transparencies for those formats, if you want to preserve a single-color background.

Quote - I see some artists achieve 1mb for their jpgs so feel my 52 kb is too small and maybe compressed.

It may, indeed, be compressed. I don't have 2012, I just have Poser 7 and Pro 2012. But, there should be a dialogue that asks you what compression you want your jpeg export to be. Tiffs are saved uncompressed. (At least, that's how mine are and I never save renders in any other format.)

If you don't get a dialogue that asks for compression rates for compressed image formats, like jpeg, in 2010, check your Preferences menus and see if there is a default setting, there.

Quote - Also is it possible to save to Tiff format and keep the background?

The background should still be there. It's just how your image viewer is interpreting the Tiff, unless you have indicated in Poser to render or export it otherwise.

Convert one of those Tiffs into a jpeg and you should see that background reappear. If it does not, then you are not exporting the background color when exporting the Tiff from Poser and you need to check your export settings there.

Not sure if I was any help, but it's the best I can offer. :D