By all means, have fun tinkering with an old computer, but don't plan on reusing parts for a new build.
15-year old memory (probably DDR?) is not compatible with any modern system. Most new motherboards also don't have the IDE port necessary for old DVD burners. Even if you find one that does, those old things don't work well. Since new DVD burners cost less than $20, it's not worth it.
There is basically nothing in there that you would save money reusing. You might be able to get some things to work, but not in a helpful way. You would need to purchase extra adapters, spending more money for less performance.
For most people, 10GB of ram is not better than 8GB. You will get the most from your memory if it is matched. Adding those extra 2GB would make the other 8GB run more slowly in most cases. There would be very few cases where they would actually provide any benefit.
You can safely reuse the case if you like it, but it will make your build harder to put together.
Even though the PSU may still function, you should not use it. PSUs fail with age and modern systems put a lot more strain on PSUs than they used to. You would not want to lose your entire build due to an old PSU burning out.