Hi Oriana,
How far you can stretch that $ depends a lot on your timeline, willingness to DIY vs. hire out, and the square footage and condition of the property.
Are you saying $10k is your max renovation budget? If you tour a home with a local contractor they can give you an idea on what you could get done with your budget. Also, would be a good idea to talk to a realtor in your area to get an idea on which improvements you should prioritize.
Lowest cost improvement that could make a big impact would be things like painting, updating fixtures. Biggest bang for buck areas to improve are kitchen and bathroom.
Its 100% dependent on what the property needs. Assuming its a well kept but outdated house (i.e. granny pad) I'd probably be doing stuff like painting walls, painting kitchen cabinets. Replace any old carpet with newer carpet or laminate in key rooms. You may not have enough $$ to do flooring in all rooms unless is very low sq. footage. Maybe replace a few old, outdated appliances that are high risk to fail in short term. You can probably also do a light update on the bathroom with a new vanity + mirror and some lighting.
If you are willing and able to DIY some of the work, and source scratch and dent appliances you money will stretch further but it will be more time and you need to be confident in the quality of your work.
Again, you need a place to have a plan but those are the "low hanging fruit"
Obviously avoid anything that needs major plumbing or electrical. In older homes this can be tricky as issues often crop up post-sale. Make sure you have contingency in your budget for the inevitable leaky faucet, broken toilet, flooded basement, dryer death, etc. etc. (I've had all four of these happen at once!)
Hope that helps.