You have a lot of options to go on the cheap. I mean actually cheap. They won't feel premium or awe inspiring but you can still get quite good (I'm currently retraining myself to use thumb, so I have both those bows below but I have the 18lbs version of the snake)
You can try the famous Snake Bow, or the Youth Titan Bow, Both capable of being drawn to 31" safely, both capable of shooting on the left or right side. Perfect for finding your particular style before choosing better equipment. Both have a reputation of being tanks in terms of durability.

I recommend This armguard

As for arrows, there are a lot of amazon sellers, with 25~30lbs being the kind of weight you want to start with, most of the sellers on amazon give you okay-ish arrows to start, I wouldn't get the cheapest option but if I had to choose, I'd get these. Do not expect to be splitting arrows though.

If you chose those 3 options, that's about 100$ leaving 50$ for a tab, back quiver or target bag. Tab/target bag should be the higher priority, all 3 would be best.

These bows and arrows I linked are for, real budget entry level "I've never shot a bow before" archers. Easy enough to pull, forgiving and more forgiving on the wallet.

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At least I think so.

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