5W-30. Synthetic is very much worth the price.
Check your owner's manual. You'll find specifications there. If you own a Gen II Solara you'll also find a (basic) recommendation on the oil cap for 5W-30. It's an energy conserving oil that will produce incrementally higher fuel mileage than a heavier oil.
As mentioned above, if your wallet can take the hit and unless you have high mileage on the car, go with synthetic if only for extended change intervals.
For a 1999 Solara v6, the oil capacity is 5 qts. of 5W30.
STP's part number is S3614. This oil filter fits a 2006 Toyota Solara (6 cyl) and other similar years of Toyota.
5,000 miles
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The oil pump is in the oil pan (aka the "sump").
5 qt
Gonna need to be a little more specific, but I can tell you it does take 5w30 oil.
dexron III
3000 miles is safest
where is the fuse box in a Toyota solara
Genuine Toyota ATF T-IV, which is fully synthetic
As you listed no year I cannot tell you what it is supposed to use. All, I can tell you is to use exactly what Toyota recommends and nothing else. And I would also ask you the question, Why Not put 5w20 in your Toyota Solara if that is what Toyota recommends?