It all comes down to what the engine manufacturer recommends for your particular engine. There are not a lot of wide variations of engine oil recommendations but they do vary with American and Japanese manufacturers.
For example, American engine manufactures normally call for a straight 30 weight conventional motor oil. Conventional means organic or just plain old motor oil. After the first break in oil has been changed, you can switch over to synthetic oil if it is a newer small engine. Older small engines such as Tecumseh or Kohler may smoke if you put synthetic oil in them.
Japanese engine manufactures take a different approach and normally use 10W30 conventional motor oil. This oil provides a greater temperature range to protect your engine. You can also switch to synthetic motor oil after the 25 hour break in time for your engine.
Motor oil brands are a matter of choice for you as the end user. It comes down a preference on price and the trust that you have in the manufacturer. I am a fan of Castrol, but it merely is my personal preference. Choose the brand that you feel is best for you.