Should i purchase a used Iphone???

I would not buy it unless you can have it in your hands before paying for it so you can personally verify it is not activation locked (I.e. has been erased, boots to the setup menu and allows you to login in with your own AppleID And complete activation).

Depending on the price and that you will need to get the battery replaced, would the new SE be in your budget?

You also need to budget $69 for a new battery in about 6 to 8 months