First, since you're looking for a baby G, visually inspecting the soundboard is simple. Anything other than a few small surface cracks? Very bad. Cracks more than 2" long? Very Bad. Can they be fixed by an expert with banding? Yes, but the deal gets diminished by repair costs.
Look for broken, frayed, bent, or unwound strings. Restringing a piano is pricey.
Play each key. Use the same hard, hit. Look to see if any keys rebound slower than others. If that happens, it will probably be in groups. If you see that, play those same keys lightly. If another key moves while pressing one, it will need, at the least, keys removed & sanded. You can do that yourself. If it's bad, the keys will need precision deplaning. That's expensive.
By touch, check the hammers. They should be firm, but not like a rock. That's easy to do on any piano. Same with the dampers.
Check the pedal action. There should be no resistance. When pressing the far right pedal, the entire damper assembly should lift equally. If not, the lever is probably bent. The far left pedal, when tested should move the whole hammer set down & forward. It shortens the throw, so it plays quieter. The huddle pedal is the sustenuto. It only works when keys are down. If that doesn't work well, you can ignore it. One has to be very accomplished to use it properly, and even good piano players barely use it. (Count me in that group.)
Play each key in octaves. In can be out of tune a bit, but if something is way off it may be the pin block has dried & shrunk. They can be fixed without a lot of cost, if you do it yourself.
Finally, watch the hammers as you play each key. The hammer should throw & the dampers lift at essentially the same time. If they don't, there are escapement issues. The entire piano will need to rebuilt. $$$$
I completely rebuilt an old upright I bought for $25 about 1983.
No soundboard issues, but the rest of the piano was a wreck. I took the whole thing apart, restrung it, recalibrated everything, sanded the keys, conditioned the hammers, & injected a polymer into the pinblock. Put everything back together. Played it for 30 years.
I replaced it when a music store owner I know offered me a $10,000 console piano, with inherently better tone, for the difference between his cost & what insurance would cover for cabinet damage on the right side. (The piano was going to go into a corner where that side would be anyway.). Paid $2,700. Sold my old upright for a grand.
So, I paid $25 for it, played it for 30 years, and sold it for a thousand.
Sorry, this reply was longer than I thought it would be.
= new reply since forum marked as read