Glad you clarified that. Are you also taking the train to Glasgow to start the Scottish leg of your holiday, or are you flying in to the airport? If you're taking the train, there are several car hire companies within a reasonable distance of Central Station. If you're flying in, you can take the bus (number 500) or a taxi to Central, or a taxi to the rental location.
If you're flying in, and hiring at the airport, make sure that you can drop off in town at no extra charge. Most national car hire companies will allow the one way drop off at no additional charge.
If you haven't driven in Britain prior to your upcoming holiday, you may want to consider hiring your car outside of the city, then returning it in the city. Central Glasgow is a very confusing area in which to drive. There are many one way streets, traffic lights at the top of hills (No fun if you're driving a stick shift!), and the dreaded bus lanes. Plus the pedestrians bent on suicide. If it's your first time in Glasgow, you may be better getting a feel for the driving outside of the city, and you'll be completely used to it by the time you return your car.
Best wishes for a safe journey!