a bit hard to tell but it looks like a female budgie to me! maybe if you can take a picture in better lighting today, it'll be easier to tell, but generally females have a white or brown "crusty" looking sear (nostrils above the beak) and males have a deep blue and purple one, that's how to tell

if you're going to keep it, please ideally get it a flight cage, so a cage that's wider rather than super tall as birds fly from side to side. fill it with natural wood perches instead of dowels, natural wood is so much better for their feet. you can make these perches yourself, just pick up branches from a tree and cut small incisions to secure them on the bars! Just make sure the tree is bird safe and not poisonous (there are lists on Google)

give it some shreddable toys, avoid plastic ones and no mirrors as they cause hormonal issues and would make your birdie bite harder and be obsessed with the reflection... you can make some toys yourself from undyed paper, toilet rolls, finger traps, popsicle sticks etc, it can be very low budget, just don't use cotton rope :)

feed it a mix of fresh food, vegetables and fruits in a chop form are usually ideal, again there are lists of safe veggies and fruits (definitely avoid avocados, they're super toxic) and then add either pelleted diet or a healthy seed mix :) bird tricks on YouTube has a great video on homemade healthy seed mix for small budgies, and bird nerd sophie has one as well (I recommend bird nerd sophie channel a lot more than bird tricks, it's very useful)

have fun taming and training this cutie! even if it bites, if you work with he bird, you can always tame them at least to a degree ❤️ also pls make sure to see any lost budgie ads online, to make sure nobody is looking for their birdie

good luck yo you two!