Best time is between April and September, with June, July and August normally having the best of the weather. Saying that you have to come prepared for all types of weather, even in August.
I would recommend a minimum stay of 7 nights.
Cost would obviously depend on the standard of accommodation and the golf courses you choose to play. You could stay in reasonable accommodation, play some wonderful links courses that don't charge the earth and rent a vehicle for around Â£900 (less than $1400 at Â£1=$1.51). Then you would have flights on top of that.
At the other end of the scale, if you play all the top courses you would be looking at around $1,500 just for 6 rounds of golf. 5 star accommodation such as The Old Course Hotel can be over $1,500 and with chauffeured transport and caddies every day you would be looking at $4,000 excluding flights.
For a middle of the road tour with reasonable Hotel, 3 top courses and 3 value courses and self drive vehicle, you should budget around $1800.
Some mistakes that should be avoided is planning to play in several areas of the country. Travel times from Turnberry to St Andrews can be almost 3 hours. St Andrews to Royal Dornoch another 4 hours. If you do not plan it sensibly, you will spend half of your golf trip travelling.
If you wanted to see a number of areas plan to play at least 2 courses in each area, Turnberry and Royal Troon, Muirfield and North Berwick and St Andrews and Kingsbarns. Alternatively, Royal Dornoch and Castle Stuart, Cruden Bay and Trump Aberdeen, Carnoustie and St Andrews.
A great website is Via Michelin, where if you go to the route planner and enter two locations and it will give you both the distance and estimated driving time.
Book your tee times for the more popular courses well in advance to secure the times that you would prefer.
If you want to play the Old Course there are several ways to try and secure a tee time. I will cover that in a separate post.
If you are planning to enter the ballot every day, it would be wise to base yourself in the St Andrews area
for most of your trip. Also check out the busy days for the Old Course. You will find that September is the worst month to try to get a St Andrews Old Course tee time as most days are busy will Club Competition finals the entire month.
Finally, the new Trump course. I have not had the pleasure of playing it yet, but will be this coming season. I can report that one of the guys I play golf with who is a 5 handicapper and has played all over Scotland and abroad played it in the autumn and said it was one of the finest golf experiences he has ever had.
Hope this helps.