I have the same generator, and have had it for several years. There are a few things I have learned from using it, and also from others here on BITOG.
First off, these generators are extremely noisy. A good saying about how noisy they are is that they are noisy enough to wake the dead. Do not even think of running it without ear protection such as ear plugs. You can buy ear plugs at Harbor Freight.
As for oil, for the very hot summers, and not very cold winters of Texas the best oil for an air cooled engine like your Tecumseh would be Mobil 15W-50 . You want the 50 weight for the hot summer days that can get above 100 degrees Fahrenheit, and the 15W will provide good cold weather starts for the not too cold winter days of Texas. If you can't find Mobil 15W-50 then use Mobil 20W-50 V-Twin motorcycle oil.
Here on BITOG there is a member who goes by Cujet who lives in Florida and he has posted that several of his neighbors had their air cooled engines destroyed by not using a good enough oil on hot Florida days.
I added a car muffler to mine. Installing it is quite a project. There are standard pipe threads built into the exhaust port that you can thread standard pipe into once you remove the muffler. The engine vibrates a lot and the first thing you should add to the threaded pipe is a flexible piece of pipe like the type that is available from McMaster-Carr.
I got the car muffler from Advance Auto Parts. It has a heat shield welded to it, and I welded some flat bars to the heat shield to mount the muffler to the bolts that hold the electric section together.
Even with the car muffler added to it, it is still too noisy to be around when it is running without ear protection. With the car muffler it sounded just as noisy when I was around it, but when you are inside your hours with the generator running on a cord 50 feet long so it is 45 feet from the house, there is a big difference with the car muffler. With the original muffler the generator was considered noisy in the house. With the car muffler the generator is only a mild hum when inside the house.
The black rubber circular gasket for the carburetor bowl tends to dry out and loose ability to seal. You can order additional bowl gaskets online from parts-tree. When this gasket goes bad the engine will idle rough and it my require the choke to be partly on in order to get it to run smoothly when there is no load applied to it.
It is a good idea to add an inline fuel filter on the hose between the gas-tank and the carburetor. A clear plastic fuel filter will let you see if it becomes clogged.