Your best update for a small full bath

A great paint color. Use white ceiling paint for the ceiling only and keep the wall color very light - doesn't have to be white, that can read too cold/sterile. If you are up to painting your woodwork, I would use a warm white color on all the woodwork/trimwork and paint the vanity to match.

That depends on what you want to spend. An inexpensive update is paint and new towels, rugs and accessories.

These might help.

https://www.google.com/search?q=updating+a+small+full+bathroom&rlz=1C1BLWB_enUS700US700&source=lnms&tbm=isch&sa=X&ved=0ahUKEwjKl4CC6qDZAhXpg1QKHdPVDpgQ_AUICigB&biw=1422&bih=684

https://www.google.com/search?q=updating+a+small+full+bathroom&rlz=1C1BLWB_enUS700US700&tbm=vid&source=lnms&sa=X&ved=0ahUKEwi37qOE6qDZAhVDwVQKHVkcCfwQ_AUIDCgD&biw=1422&bih=684&dpr=1.13

Lighting! The fastest, cleanest change you can instantly give to update any bathroom is to change out the most likely dated, old yellowy dim incandescent light bulb fixture with a new fixture with LED lightbulbs. If budget permits swap out your old simple on/off light switch with a dimmer switch.

would you mind submitting a photo...then we can see what your working with..

New paint changes things a lot. A new fabric shower curtain (with a plastic liner), scatter rug(s), towels will change it over in minutes. Accessories can be added to make a big difference.