Travel history is only bad/hindering to a case if it is to countries that are viewed as high risk/suspect to terrorism, etc.
Otherwise travel history is actually very good because it shows that a person was admitted before to various other countries, and that person returned rather than living their illegally. Just make sure that this is all entered in the personal history section of the forms on your application. If someone misses out on including the travel information, then it looks suspicious.
My husband had travelled to Malaysia, Thailand and Dubai for work trips, all no more than a week, but his checks did not take long (guessing 4-5 months, and 1 wk after ppr).