Best and cheap?? Cheap is Pattaya but the beach is not the "best!" Easy to get to from Bangkok. Access to malls, street vendors, cheap hotels, movie theaters, supermarkets, nightlife, good restaurants, beach good for sunbathing and jogging, hospitals and dentists available. And cheap 10 baht transportation. Beach sucks for actual swimming!! Pools available. Swim nearby at Koh Larn, Jomtien and Naklua. Only costs 113 baht for the 2 hour bus ride from Bangkok. Stay on Koh Larn island but have cheap access to Pattaya for only 30 baht on the ferry.
Or go to Koh Phangan, mingle and drink and do drugs with (mostly) teenage boys while looking at the moon, etc.
Hua Hin. You can reach there by train, bus or taxi. Not as cheap as Pattaya but the beach is nicer.
Want to be more remote. Koh Sukorn.
You will have to do some work on your visas. You can't stay in Thailand as long as YOU want. There are regulations. Even if you can get 30 days free entry or not depends on the passport you travel under. (Visa charges in the near future may be waived to entice more tourists. So keep up with this change. Depending on your passport, you can stay longer for free.)
You must establish some sort of budget to get a daily cost for hotel or whatever. You can not just sleep on the beach like a common vagrant. When you ask for hotel suggestions mention how much per night you want to spend on a room.
Helpful travel forums:
Some hotels have free wifi - some do not! But there are many internet shops available at low prices.