:welcome:
There are direct replacements that will drop strait in , plug up and go.
And then there are engines that will fit but will require a little fitting, usually on the wiring.
Any Briggs single will drop in & bolt up but you might need to swap out your alternator if you want the wiring to plug strait together
Any Kohler Courage or Command single will drop strain in and bolt up but you have to fit new plugs to the wires.
Most Honda & Kawakasi will be a similar proposition. although the bolt patterns on there are a bit different and the control set ups vary.
So it all depends upon how much work you are willing to do and what level of skill & understandings you have.
Your engine has a 1" drive shaft that was 3 & 5/32" long'
So any engine with the same size drive shaft can be made to fit.
After that you need to look at electrics.
If the mower had a manual PTO then any capacity alternator will do you fine , though a 3 amp will struggle to keep the battery charged if you start & stop a lot.
Briggs used the same mounting centers ( and flywheel castings ) for all their engines so alternators swap out real easy.
Kohler did the same.
If you have an electric PTO a 5 Amp will almost keep up but anything larger would be better.
A couple of places I use regularly are
http://www.smallenginewarehouse.com/Repower-Old-Equipment/Repower-Craftsman/
and
http://http://www.smallenginesuppliers.com/shop/html/pages/briggs_vertical_shaft_engines.html
Both of these compnies do superceeded engines.
Your engine was classified under the old system so a new engine marked 19Hp will have the similar power.