There’s not much consensus regarding what differentiates a purse from a handbag. I consider anything with a shoulder strap to be a purse.
Assuming this is your first bag, I’d go with a medium size purse. It’ll be big enough for all your stuff but not overwhelming, and it’ll have a shoulder strap. It’s your do everything daily driver. I have several.
Handbags come in all sorts of sizes. Since they lack a shoulder strap they’re not as versatile. Not hands free. Easier to steal. I don’t own one and doubt I ever will.
A clutch is very small and really limiting. Enough room for lipstick, your ID, a credit card or cash, and maybe your keys. Most women only use them for dressy events and such. I don’t own one but expect I will someday.
If you’re a practical girl, buy a purse. If you like collecting things, buy them all….in multiples!