I traveled through Malaysia by train going from Thailand to Singapore.
It was about $40 from Bangkok to Butterworth. The ticket was easy to get at the Train station in Bangkok. Train left at midday and arrived in Butterworth in the morning. The train was comfortable, modern and the bed folded out to be large and comfortable.
Once you arrive in Butterworth, a quick walk over to the ferry station and a $3 ferry to Penang. You can leave your bags at the train station for the day.
In Panang there are cheap places to stay, cheap beer and delicious food at the Malaysian markets. There is rain forests, beaches and really cool temples.
I took a night train to Kuala Lampur and arrived at the really nice train station. The train station is next to some great hotels where you can get a great view of the city. The subway or metro is also at the train station and you can go all over town.
It’s something like a $100 bucks to go up and it does sell out so you may need to get the tickets in advance if you only have a day or two in KL.
The Television tower has great views of the city and it is more affordable than the towers. At night you can get a great view of the towers.
From Kuala Lampur there are trains to Singapore. They are cheap but if you don’t get a sleeper, it will be an uncomfortable ride.
You arrive in Singapore quiet far from downtown but it is close to a bus station. The way through border patrol is quick and easy. A bus will take you to a metro/subway station from where it is easy to get to downtown. There is a nice Malay style food market at the bus-station where you can get a bite to eat before the hour bus ride.