Audit firms do accept internship, provided your results are good.

If you intend to take Audit firm as your "spring board", Big4 is a popular choice, but there are trade offs compared to small/mid audit firms.
If you intend to become a Partner of a Audit firm, Big4 again is a popular choice, but not necessary better.

Working in Big4 makes your resume looks good to some extend

Small/medium sized audit firms are usually locally established companies, their clients are often small/medium sized companies. Big4 companies usually audit Fortune 500 companies and many MNCs. So it depends whether you want to audit small accounts or big accounts.

Auditing small accounts has it's benefits too, you get to be exposed to full set of accounts. Where else, in a Big4, the first few years, you're gonna be audting a fixed area, like bank, AR, Inventories, or AP etc... or worse is statutory accounts, or holding company which is idle of activities, nothing much to learn from. On off peak season, if you're too junior, they might even ask you to do lots of photocopying & filing work for Seniors Sometimes it depends on your luck which client you're gonna be assigned to, so you gotta be good friends with your manager.

Working in Big4 has it's perks too, you get to be exposed to many clients, so you would have many contacts. You build a good social network of colleagues and useful contacts This is hard to find in small/mid sized audit firms.

Nevertheless, if you can't stand finding yourself working until 4-5 am in the morning just to rush an account... audit is not for you Good Luck in your search for a better career.