Things you should have:
Enough bibs/shorts, jerseys and socks for a week's worth of rides.
Floor pump.
Mini-pump (and/or CO2) and spare tubes.
Multi tool.
Tire boot.
A method of carrying tubes, pump, boot and multitool. (phone and $ are good to have, too)
Cages and bottles. (number depends on ride length and frequency, but they are cheap so get plenty)
Comfortable shoes, saddle and helmet.
Sunglasses.
Spare tire.
Tube patches. (the glue on kind, not stickers)
Proper gearing. (does your cassette and chainring set up match you terrain and abilities?)
These are things that are also nice:
Gloves, jackets, arm warmers, etc. (if you want to ride in conditions that require them)
Cycling computer.
Home tools and stand.
Extra spokes.
Spare chain.
Spare wheelset.
If you don't have any of the items the first list I would buy them right away. The second group will depend on your personal preferences, but I would get anything you want/need there covered before spending money on upgrades, too.
After that, as others have said, ride some more and if competing get an event or 3 under your belt. By that time you will know what else you need or need to upgrade.