I use Milsek furniture polish and cleaner on my furniture.

If there is any small scratches or wear spots I use Old English scratch cover first.

They left you some nice pieces.

Are you talking about updating them or just cosmetic spiffing? In the bedroom, I'd remove the 2 narrow mirrors and hang either a large piece of art or a larger single mirror (if you need a mirror there).
I think the chairs and table are quite nice, but the china cabinet is a bit dated, so I'd probably remove it and use it elsewhere or sell it. If the top comes off, you could use just the bottom as a buffet, with art above, which would be an updated look.

Congratulations on your new home. The furniture pieces the owners left appear to be lovely. You have the advantage of options: continuing to use as is, or making changes without fretting over family “heirlooms”.
My thoughts: 1. don’t make any changes to the furniture now until you figure out the rest of your space. 2. Very much like the dining room table and chairs - however you may want to re-upholster chairs. 2. Breakfront - could in the future be professionally painted. I know there are some people that have a business of taking “brown” furniture and making it work for today. Alternatively, is there another space it could go? 3. Bedroom furniture- would keep both, but not in the same bedroom 4. Bedroom mirrors - would think about repurposing elsewhere. Best wishes.

I am actually going to put the bedroom furniture in the guess bedroom. Thank for all the sugesstions, appreciate it.