I think the best advice I have for you is find a team first and get comforable with each other.
Get involved with them and train without a dog. You will learn a lot. Some teams may have an immediate opening for a future dog handler and some a wait of a year or more, and there you are on your own not getting the best help to get on a good start if you already have the pup and not the pup is taking time you need to invest in all the non dog related training, not to mention helping with existing dogs on the team who have first priority for training time. The folks on the team are going to be the best folks to help you pick out the pup or young adult, too!
I will say the last thing any one screening SAR inquiries wants to hear is "my dog needs a job" and "I have this really great dog".....And most teams really don't want you to start with a dog that is too old because it is you they are interested in.
Then as time allows and not before get the puppy or young adult dog for training. Starting a career and getting settled, you have a lot on your plate first.
Depending on the team, they may want you to prove you will stick with it before they let you bring in a dog. Nothing about you but about the typical volunteer whose vision may not match the reality of what they were expecting. Disaster work / Wilderness work? Wilderness teams are much more common and deployments shorter in duration and more frequently (typically a day or two vs several weeks for disaster work). Some disaster dog handlers have had a dog live out its whole life without a deployment [though the wild weather and all recently seems to be making sure everyone gets some action]
The disaster screening test used by FEMA is for a young adult candidate. www.disasterdog.org
gives an idea though..that is the test our wilderness team uses for incoming candidates that are fully grown. For a puppy the PAWS working dog evaluation is better than nothing but ANY puppy is a gamble.
When I got mine, the breeder knew that if was not suitable for SAR that I would find him another home. She understood because she is a working dog handler herself . Phew. He is awesome....but we still have a hip, elbow and back x-rays to get through in July and you know no problems knock on wood but that is two years invested....you have to think (with a puppy) what is the back up plan if it does not work out? We have all spent time on pups/dogs that we wound up washing out of the program because the stakes are that high.
Based on the statement "having a child that likes to run" - I assume you have a young-un, the kind without fur. The other question if you have a small child is the amount of time and things missed. I waited until mine were older and still
got resentment because I missed some band events, etc. It is a real stress on the family. OTOH, sometimes I wish I had started this when I was younger than I was when I did. It is a lot of time. With a little one you would have to have solid back up plans because they will expect you to go when called.
OTOH if you want to go ahead and get a pup because you want one. Then do. Realize you are looking at a higher drive working dog and one with good hunt drive. You can still raise it and do some basic drive building and obedience training and if it winds up working out, yay. And if not, get another dog.
So I am not trying to be discouraging just painting a real picture and saying "try it first"
- if you want to get a GSD, that is fine. FWIW-we don't let folks "carry" on a search; if it is a dicey situation, we want the police flanking for us and nobody does something if they don't feel comforatble with it. We also don't send out people alone.