We started about a month after finding out gender. I wouldn't go overboard until after the baby shower. We were so blessed by our family and friends. I was doing research on the big items from the beginning though! I had no idea what we needed for a baby.
I am 32 weeks and was thinking I would start in 3 weeks.
For me, with number 1, I bought a crib/matress (with a changing table attached to the crib) and a dresser about 5 months in. I also set up her room that month, painted the walls etc. I didn't want to wait until I was too big to move. Also I got a bunch of hand down clothes from friends right after knowing the gender. I didn't buy any clothes until after the baby shower... I did have a pack of diapers probably at 7/8 months to be ready... and got some things as I got good deals along the way like a baby bath... some baby blankets I liked... a couple cute clothes while shopping... I got the stroller/car seat through work at 7 months... and yeah it was stress free. I wanted all the essentials by 7 months in case she came early...
I made a list of things I wanted to get then started keeping my eye out for deals and sales when I hit the 12 week mark, didn't buy any of the big/expensive bits until I passed the 20 week point, then have slowly just added to it. Probably felt I had enough stuff by 30 or so weeks, anything now is just extra