There are many effective ways to travel the country with scooters, motorbikes available to rent across the Kingdom of Thailand but buses and trains are generally the safest and cheapest way to move around.
Buses cover most of the country and are the cheapest form of transport available. Every city and town linked by bus has a BKS station, even if it's just a wobbly signpost at the side of the road.
There's a 4500km rail network connecting the country's four corners. Trains are ideal for shorter journeys but are often a slower alternative to buses on longer trips. Sleeper trains to any part of the country cost from around 1200 THB down to 300THB depending on whether you travel 1st or 3rd class. In Bangkok, you also have the BTS elevated train and MRT underground train which are cheap to use from 20-40 Baht but the trains do not cover Bangkok extensively.
Taxis are all over Thailand and usually start from around 30 Baht. In Bangkok, no trip should cost more than 150 Baht. Motorcycles taxis to get you a short distance are fine but long distance can become expensive and dangerous.
Tuk Tuks are good as a novelty ride and for the thrill but are generally more expensive than taxis unless you haggling skills are up to it.