If the seller's genuine, they'll be happy for their car to be poked and prodded by a garage.
Which garage you choose is down to your experience of their ability, but a rule of thumb is to stick with what the garage knows best - don't use a Peugeot specialist to check over an Audi, for example.
Cost is usually set by the garage's hourly labour rate, plus a bit extra for their know-how. Don't expect any come-back if you buy the car and it falters.
For
Good specialist knowledge
Can be cost-effective
Against
Don't expect any come-back
Persuading the vendor to drive to a garage