Start out by wearing what is comfortable and in your wardrobe. It is much more important that you actually get out there and ride, rather than sit at home planning your cycling wardrobe.
You said you only ride once a week, but you did not specify the ride conditions and circumstances. Commuting in mild weather, recreational riding in sunny weather, gravel grinding in a state forest, etc.
As you ride, you will discover how committed you are to cycling, which will in turn dictate what you want or need next. Some people, like me, are psychologically predisposed NOT to wear spandex. As such, the cycling shorts I have could pass for ordinary shorts.
In terms of what's most important, first things to get are a helmet (if you desire), gloves, and eyewear. I recommend full finger gloves, even in warm weather, as they protect your hands against nicks, scratches, and scraps.
After that, a cycling jacket for weather and road protection plus visibility so some reflective surfaces are a plus. Shop in the store so you can try it on to ensure it fits and suits you.
Your backside may next demand padded cycling shorts or cycling shorts with separate padded underwear. You may also be thinking about a better saddle.
At some point, you may get the desire for clips and shoes. This is a serious transition as one can fall over and go boom if one is not unclipped. I bought a set, and they sat for weeks until I broke one of my conventional pedals. That forced me to cross over to clips. And you will eventually fall, but you likely will walk away will just a bruised ego. I did.
Finally got a jersey, one, in 2014. However, I mostly still ride in casual clothes, including T-shirts during the summer.