Need to get an iPhone 3GS repaired. What are my options?

Find a reputable 3rd party repair shop. Apple won't work on it. It's too old. They no longer have replacements or parts.

Or just find one for sale on eBay. Should be pretty cheap.

Replace it. It has no value.

If this is a Verizon or Sprint model phone you will only be able to use it as a phone for another 12 days.