I like to start my IVs in the hands or feet first. I try to leave the upper arms and antecubs alone for future placement of PICC lines. On the micropreemies I do the same but it is much easier to go for the saphenous on those little ones since they are big and easy to see.
After I get the flashback when starting an iv I like to take my needle out (saftey needle of course) and (as someone else mentioned) float the catheter the rest of the way in. If I have an extra hand, I will have someone slowly flush while i guide the rest of the catheter in. I learned this from more experienced nurses. Usually when people try to advance the catheter while the needle is still in their veins blow because the needle is shredding the vessel.
Oh Yeah I like hands and feet especially on bigger babies because I can bundle the baby in blankets and leave the extremity exposed. THsi helps to better control the baby since the bigger ones fight kick and scream
At my institution you are supposed to try 2 or 3 times then ask someone else to try. However that is not always possible and you have to try until you get it. Having to wait an hour for someone to be able to help you get an IV canbe a pain when you pt is NPO and you have to cut their fluids off since you don't have an IV and all your IV meds/atbx are due right when you IV went bad.
I like to use our little rubberband tourniquets Unfortunately, I must admit, I have started to favor using a transilluminator when I start my IVs.

However I was trained to get IVs without the use of the transilluminator.
Hope my babbling helps