Mobile 1 is a BRAND of synthetic. 10W-30 is a WEIGHT (actually a multi-weight)
Check your owners manual for the correct weight of oil for your vehicle. Sometimes it will recommend a different weight for different seasons, or different types of criving (heavier oils in hotter weather and higher demand driving, lighter oils in colder weather).
For example, my car calls for either 5W-30 or 10W 30 depending on driving consditions and weather. I use the lighter of the two (5W-30) to maximize fuel economy.
Any car built after the mid-90’s can use synthetics. However, transitioning an older car that has been using regular oil to synthetic CAN cause damage. A new car, even if originally filled with conventional oil, switched to syntheic is not a problem. And for modern small high-performance engines with very high heat and conplression, synthetics are generally recommended.
Also, one final note, you should generally “short change” the first load of oil in a new car (1000 miles). This will help flush out any manufacturing contaminants (metal shavings, debris, etc.) from the manufacturing process befor ethey can spend 3000-5000 miles scraping the inside of your engine.