I'd say you'll do best by filling your minds and meditating on things true, noble, reputable, authentic, compelling, gracious—the best, not the worst; the beautiful, not the ugly; things to praise, not things to curse.
What we think about matters. When we have thoughts that are constantly gravitating toward worry - it becomes an all-consuming process that eats us up! Did you ever really think about what worry is? When we are spending our time in worry, we are really focusing all our time on reviewing over-and-over again what we have absolutely no power over! That seed of doubt, fear, frustration, etc., soon becomes a full-grown tree of worry if we continue to mull it over in our minds. We have no control over it, but it soon begins to control us.
You need to know this one thing: If we can get our minds constantly in a place of activity (worry), then we have less ability to tune into what God wants to say to us about the situation. Activity shuts down the communication avenue. That is why Satan is delighted whenever he sees us engaging in the thoughts of doubt and worry! The term "worrywart" actually comes from a comic strip in the 50's in which a character in that strip was constantly causing worry in others rather than being worried himself. There are both extremes to worry (fretting) - being so consumed yourself, or shifting it to others in order to avoid it yourself.
The first thing we need to embrace when dealing with our thoughts is that they are a choice. Have you ever been to the local home repair stores during planting season? In the gardening section, there are these turn-styles with tons of packages of seeds in them. Within each package you will find between 12 seeds (if you are planting something like pumpkin) and hundreds of seeds (if you are planting radishes). One seed is large and easily recognized. The other is quite small and many may slip through your hands unnoticed as you examine them. The same is true with our thoughts - there are big ones we easily recognize and dismiss. There are also small ones, not so easy to detect, but nonetheless capable of producing a bumper crop of growth!
Whenever we give up control of our thoughts we have the potential of ending up going down a road that we would have rather avoided. It is a road often marked with lots of potholes and ruts that will get us "stuck" for a long time. Did you know that a rut is a track worn by habitual passage? Take that and apply it to your thoughts - what "track" have you created in your thought life? That which consumes our thoughts soon consumes our heart. Outward circumstances impact what we internalize. Internalized circumstances soon become worries. Worries soon become tracks well-worn by habitual passage!
Paul tells us that we have power over our perspective in life - it begins in our thoughts. When he begins with the idea of "think on these things", he is assuring us that we have the power to choose our thoughts. Perspective is the relationship we attach to the various input we receive - when we are actively involved in choosing how we view the various input, we learn to control the impact they have on us. You have heard the saying "mind over matter" - I'd like us to begin to realize that it is "what comes into our mind matters"!
Worry is often a point of conflict in our lives - our minds think one thing, our heart knows another. We choose our response to that conflict based on the thoughts we allow to become the most central part of our focus. The same is true of hatred, anger, or bitterness - our minds entertain the thoughts of how we have been wronged, our hearts are challenging us to forgive as we have been forgiven. We choose our response to that conflict based on which thought we give the most attention to. There is no better place to have boundaries in our lives than in our thought life. When we learn to declare some roads as "off-limits", we are less likely to end up in the ruts of habitual passage!