The following link gives a broad over view of what Iceland is like in September and gives examples of what to pack. https://adventures.is/blog/september-in-iceland-all-you-need-to-know/
In September, the average low temperature is 43°F (6°C) and the average high is 52°F (11°C). But Iceland is famous for its quick weather changes, so don’t be surprised if one day you wake up to 25°F (about -4°C) weather or even temperatures in the high 60’s (around 20°C). You can prepare but you can’t really know exactly what the weather will do.
Snow is unlikely in September, but the average rainfall amount is 3 inches. Bring waterproof gear.
Iceland is 5 hours ahead of us. (Ex. if it is 5 pm in Kansas City, it is 10:00 pm in Reykjavik)
We would recommend that you pack layers. Pants, long-sleeved shirts, sweaters, jackets, hiking or walking shoes, and be extra prepared for cold and rain if you plan to camp. Don’t forget your bathing suit so you can enjoy the local pools and thermal baths. And as for rain gear, umbrellas don’t often stand a chance against the Iceland winds so it’s best to rely on rain gear that you can wear and always have it on you in case the weather decides to surprise you.
Food is terribly expensive in Iceland. It is an island so getting a hamburger and fries at a gas station may cost you $40. Iceland is known for their hotdogs (very different from the ones here in the states) and may be a cheaper food option. Stopping at a grocery store and cooking in most nights is HIGHLY recommended (Bonus supermarket is one of the cheapest markets, 10/11 is a super market located near KEF airport and has higher prices due to convenience.)
Icelandic is the native language, but many speak English.
Currency in Iceland is the Icelandic Krona. (1 USD = 122.75 kr) Debit/Credit cards are widely accepted across Iceland.