Sometimes it takes some doing, but I'm able to start my 1923 touring. I doesn't sound at all smooth running to me, but I don't have a comparison due to lack of experience/exposure. If I were to figure a way to post a sound bite, could a good guess be made on where to focus my attention?
Maybe, but it would probably still be speculation. Tell us where you live. Maybe someone is nearby and could help you in person.
You could take a video and then post it to YouTube. Just copy the link and post it here.
Starting and running have fairly basic requirements - air, fuel, and spark. Since you mention it takes some time to get started, it could be one of those.
Has your 23 been sitting a long time? My two biggest problems were a carburetor rebuild and the animals that used the tailpipe as nut storage.
I'd recommend following a checklist such as this one to do the once over on all the things to check, not just the engine (even though getting the T to run well is so rewarding compared to some of the other things!).
This forum is a great place for expert advice from great folks.
I also go on YouTube to hear how other Ts
Of course, nothing beats having a fellow T-bee stop by and take a look-see. I had that good fortune several months ago.
Just as cars look better in pictures, they sound better, or at least different, in videos. The microphone isn't good at picking up all the various sounds a Model T makes. Brooks is right. It's best to have an experienced Model T guy listen in person.