I’d look for stone buildings, thick walls, but not listed. If they’re listed it’s hard to get permission to put in double glazing and such
You only have to consider damp if they are low lying really. Again if they’re not then they can be sealed, but this often affects the long term durability of the older building as they were built to breath. damp occurs if a building is not well ventilated, so make sure it is.
New builds as PP have said will be the best from an energy efficiency point of view. But the internal walls are plasterboard between rooms, and the spaces and gardens often smaller.
BISF buildings as they are non standard construction can be difficult to sell as not all mortgage companies will offer a mortgage on them.
Older timber buildings if they are listed are cold…trust me I live in one. But if they are not listed can be upgraded to offer excellent up to date energy efficiency without having to add extra layers and loose floor space. The rooms are larger but some more cottage types have low ceilings as people were shorter.
Traditional Victorian or Georgian houses of brick if they are double glazed and have roof insulation are an excellent alternative to new builds, Georgian houses tend to have larger rooms with higher ceilings.
We don’t have issues with termites or moss. We get woodlice if there’s wood in a property but they are just wood lice. Older buildings can get infestations ( beetle ) which eat away the wood if the building is damp but is easily treated and they only eat the soft outer wood, never the harder core which is actually doing all the structural work.
Surveys will pick up any issues that could be of a concern.
Plus each property in the uk can’t be sold without an EPC showing how energy efficient it is. It will be on all the info you see when you spot a house you want to look at.
Good luck OP