My must have list for my bike sadly exceeds $250, but it'll give you a place to start.
Floor pump; tire levers, patch kits, CO2 inflater and cartridges and/or frame pump, extra tube(s), saddle bag, water bottle(s). Multi tool or hex wrench set and lube. Decent pair of shorts, helmet, gloves, sunglasses, jersey (short or long sleeve depending on the weather). Sunscreen.
Other things that are definitely helpful: Bike jersey, cool and cold weather gear (arm warmers, long sleeve jersey, windproof/water proof jacket, tights and knickers, full-finger gloves, wool socks, headband), chamois cream, a bike repair manual, bike computer, cycling shoes, and rear tail light (I'd almost put this on the must have list), and lightweight jacket.
I'm sure I'm forgetting something. I'm embarrassed by how much bike gear I have, but truth be told, I use all of it pretty regularly.
Live with intention. Walk to the edge. Listen hard. Practice wellness. Play with abandon. Laugh. Choose with no regret. Continue to learn. Appreciate your friends. Do what you love. Live as if this is all there is.
--Mary Anne Radmacher