If this is a course I haven't played before or rarely play, I'd use the same tees. The first round will be used to figure out where features are and learn each hole's layout.
I've used alternate tees on our local 9-holer. I'd like the club to add more tees to change things up but there is limited land, very limited interest and no funds.
If the 9-hole course is going to be built, then I'd strongly encourage multiple tees and double greens on the par 3s. A small town near me (Adrian, MN, pop. 1,200
http://www.adriancountryclub.com/course.html, see their website for some pics) built a 9 hole course about 30 yrs ago. It's a very enjoyable course. They have double greens on the par 3, some par 4s become par 5s and vice versa. The back tee yardages are as follows:
#1 503 yd par 5 #10 422 yd par 4
#2 409 yd par 4 #11 370 yd par 4
#3 393 yd par 4 #12 506 yd par 5
#4 545 yd par 5 #13 417 yd par 4
#5 371 yd par 4 #14 317 yd par 4
#6 187 yd par 3 #15 164 yd par 3
#7 444 yd par 4 #16 514 yd par 5
#8 172 yd par 3 #17 156 yd par 3
#9 322 yd par 4 #18 433 yd par 4
Out 3346 yds In 3299 yds
Hopefully the attachment to work. It's a heck of a course for small town: