Typical Budget?

Where are you traveling from and to? Does your request need to include airfare?
Take a look at Booking.com for where you will visit for an idea of hotel prices. Please come back with where you are going.

More details would be helpful. How many people are traveling? How many people per room? Would you consider renting apartments? Do you drink alcohol? What kinds of sights/museums do you plan to see? How are you traveling around (car/train)? Which cities are you going to?

Check out the Scotland Explorer pass for savings on museum entry fees.

We are a family of 4 and have stayed in nice 2br/2ba apartments in several countries for less than 150€/night using booking.com or AirBnB. This is our biggest cost saver. For food, figure what you would normally spend per meal while eating out at home and add 20%. Save some money by splitting a pizza every now and then. Don’t pay for breakfast at a hotel, walk down to the local bakery.

Basically I need to know if we should budget $2000 a person or $9,000 a person. :)

Closer to the lower figure, especially if excluding the cost of getting there and back home

Take the hotel cost out of the equation by going to booking.com and entering dates for your key destinations within your travel period. I imagine late September isn't quite as busy as the peak period, but it may be busy enough that lodgings in the most popular rural areas are full or nearly so. They may be more costly than you are imagining.

Do you plan to rent a car? That will allow you to stay in less centrally located lodgings when you're out in rural areas; they may be less expensive than the ones I needed to use because I was traveling by train and bus. If you plan a car, price it on AutoEurope, Kemwel and/or Gemut.

Entry fees can be fairly substantial. It costs a lot of money to maintain a castle. Once or twice I opted just to pay to see the garden because I really don't care for most castle furnishings.

If you're going to use public transportation, note that train fares in the UK often vary greatly depending on how early you buy tickets. The Advance fares--think of them as not changeable/not refundable, though I think you can sometimes change them upon payment of a lot of money--can be as little as 1/4 or 1/5 the cost of the walk-up fare on the day of travel. I suspect bus fares may also be somewhat variable, but I'm not sure about that. If you wait to buy train tickets after you arrive in Scotland, you may spend considerably more money. I believe the train fares from Edinburgh to Glasgow are fixed, however.

I like nationalrail.co.uk for researching rail schedules and fares. I used travelinescotland.com for buses. TravelineScotland also covers trains, but I got some anomalous results there that disagreed with the NationalRail website, so I didn't quite trust TravelineScotland's train information.

Thanks for the replies... Here are the answers to the above questions!

There will be 3 of us (all 3 in the same room); I live in southern California and the other 2 live in Montana. I don't need the cost of airfare included in my budget, as I can figure that out pretty easily. Was just looking for everything while we're there...lodging/food/etc.

Yes, we do drink.
Yes, we're totally open to any and all accommodations (hotels/B&B's/VRBO or AirBnB/etc).
As far as things we'd like to do/see... This will be the first time for all 3 of us. We were thinking of flying in/out of either Edinburgh or Glasgow, staying for a couple of days, then taking the train to Glasgow or Edinburgh (whichever one we didn't fly in to), renting a car and doing a loop up to Inverness/Skye then back down. Other than that...we're still in the beginning stages of research!! I have the Scotland book and have started reading for ideas! We're not huge museum/art people, but a castle or two would definitely be in the plans.

Always willing to answer more questions. Thanks so much to you all!!

Do take a look at booking.com. You can set filters for factors important to you and read reviews by people who are guaranteed to have stayed at the properties. You'll find B&Bs and some apartments listed, as well as hotels. I don't know of any better way to figure out what you'll need to spend on lodgings than to do that. You needn't reserve through booking.com; sometimes you'll get a slightly better deal by going direct. But the booking.com research will be very useful in building a budget.

I found it very difficult to get well-priced twin-bedded rooms in the coastal towns and island towns served by public transportation, and I was booking for July six to seven months in advance. Don't wait too long; triple rooms are not all that common. However, I know that a lot of the Premier Inns (which will not necessarily be listed on booking.com) have a comfortable day-bed that can be made up for sleeping. They are not sleep sofas; they have regular mattresses. Premier Inns are what I call "business-class hotels". They are functional rather than charming. But the rates can be very reasonable if you book well ahead of time. They have even lower rates for non-cancellable reservations, but I have never dared to do that. Unfortunately, Premier Inns are mainly in the cities. One other thing: I haven't checked recently, but there have been persistent problems with the Premier Inn website changing the reservation dates as the booking process goes along. You have to pay very careful attention and perhaps use the "Change" function more than once to get the reservation correct.