When playing both Solo and Team Survival Games, I start with the class that gives you a chestplate because I usually find a weapon 90% of the time at the Cornucopia within the first 20 seconds of the match. I open the nearest chest at the middle, and while looting, I usually go for any weapon first, TNT second, then armor. I don't tend to grab any food right off the bat because once the 20 seconds are up, there are usually people still looting or organizing their inventory that I can eliminate using a well-placed TNT. Usually the TNT scares away any extra people, so I can safely loot any eliminated players and unopened chests for any food or other items that I may need in the long run.
If I don't get any TNT, I quickly identify someone who has put on any good piece of armor (Iron armor or better if Normal Items/Diamond armor if Overpowered Items) and rush them down immediately. This prevents them from becoming even more of a threat later on down the line, as they usually won't have a full set of armor to protect them after invincibility ends so it is easier to take them down.
I have a lot of PvP experience, so my strategy is usually to take control of the Cornucopia after invincibility ends. This strategy has awarded me with many wins and a pretty good K/D since a lot of people don't know how to deal with an aggressive player right off the bat. However there have been plenty of rounds where I get unlucky when looting and find nothing useful, so I have to run away and play less aggressively.