Going by the specs posted, you should be safe with a 350w power supply. It looks like your motherboard has an 8-pin EATX12V connector, and your old PSU probably has a 4-pin plug. That should also be ok. I don't know the age/condition of the old PSU, but it can probably be used as a stopgap should you choose to get a newer power supply later on. Though, a higher watt PSU is recommended if you decide to get a better graphics card.
Oh, that is a problem. Didn't realize your PSU is that old. Even slightly-newer-old ones have a "20+4 pin" for the EATXPWR, besides the 4-pin EATX12V. If that's what you're missing, you'll have to get a new PSU for that system. Depending where you shop, you can get a decent one for about $30-40.