Hi there! That sounds like an adventurous trip! Here are some travel tips meant for you.

Best Time to Visit:
The best time to visit Gongju, Buyeo, and Iksan in South Korea is from April to June and September to November. These periods avoid the summer monsoon season and the cold winter, plus the Spring and Autumn colors are fantastic.

Route and Accessibility:
These cities are well connected by public transportation. The Gyeongbu line KTX train or express bus from Seoul to Gongju would be convenient. From Gongju to Buyeo, there are direct intercity buses, and from Buyeo to Iksan, you can take the train or another intercity bus.

Accommodation and Booking:
The cities have a wide range of accommodation options, from budget guesthouses to mid-range hotels. It's best to book your accommodation in advance, particularly during the popular travel seasons of Spring and Autumn.

Clothing and Essentials:
Pack comfortable clothing suitable for variable weather, good walking shoes for exploring, a lightweight waterproof jacket, sun protection, a good camera, and an adaptor for South Korea's Type C and F power sockets.

Health and Safety:
South Korea is generally safe for travel. However, ensure you have travel insurance, are updated on routine vaccines before every trip, and have emergency contact numbers at hand.

Local Etiquette and Respect:
Koreans value respect and modesty. It's common to bow when you greet locals, and use both hands when giving or receiving items. It would benefit you to learn a few Korean phrases and the culture.