We did have the XRM here maybe 12 years ago, they were the first small clutch bikes released in Asia. These kind of bikes ( Suzuki Raider, Yamaha Sniper etc ) now command high prices as they are the chosen bikes for the teenage drag racers, you don't see many of them on the streets these days. They are also widely stolen, so not the ideal bike for riding in Asia.

You are now talking about a 125cc bike ? You may have some difficulties taking the bike into Laos. Small displacement bikes from Laos are prohibited from crossing into Thailand, therefore Laos customs have a 'reciprocal ban'. This isn't to say that small Thai bikes haven't been seen there, its just not officially permitted.
I will hopefully confirm in a few months that Malaysian bikes smaller than 150cc can be taken over the border, if so, this would be a good suggestion.

If you buy a bike in Thailand that you won't register yourself in your name then there is an official document ( its not just a letter ) - posted on rideasia, however, there are reports that this document does not guarantee entry. Just to point out this isn't a letter saying it wasn't stolen, its a letter from the current owner giving permission for the bike to leave the country. You will not be the official owner until you register it with the Dept. Land Transport.

In my opinion the best bike for your purpose is a CRF 250.

Under $2500 US .. easy to move across borders, little depreciation and probably easy to sell after. You can load them onto trains, send them through the postal service and transport them across rivers on bamboo rafts. However, they don't make them in MY. They need to be bought in TH.

If you want something similar from Malaysia, it will be the KLX-250 but they command higher prices than the CRF and if something goes really wrong, although many Kawa dealerships in TH and MY, there is only one in Vientiane, Laos.

If you are talking about a trip to Indo, you can get a carnet from the Malaysian AA - you can get one for a Thai bike from them, apparently, but again you will need the bike in your name.

As others have pointed out in other forums, Thailand is your best chance to find the cheapest bike, but if you want to have an easy life, then just take the time to register it yourself, its not easy or quick, but worthwhile in the long run. You wouldn't expect to overland from Europe on a bike that wasn't reg'd to the rider, its no different here.

If you talk about it being a bit of a frugal trip, then perhaps better to understand your limitations and plan accordingly.