You only need an inverter to run AC (115 volt) stuff. For phones and laptops, chargers which plug into 12 V (the common "cigar" DC outlets) are readily available and are more efficient than using an inverter and AC charger. Most RVs have lighting (and other basic infrastructure like water and heat) which uses 12 V.
There are TVs which run on AC, and there are TVs which run on 12 V DC, so it's hard to say what you have/need. A 500 W inverter should be way more than enough to run any modern TV. If you're going to buy an inverter, I strongly recommend you get a "pure sine wave" one. Their output is similar to that from the outlet at home. Cheaper ones are hit-or-miss whether they'll work with electronic devices.
