Just sampled my first batch - IPA - help/thoughts?

Started my first batch while I was home in California. After waiting 2 weeks for fermentation and 3 weeks after bottling, my beer arrived in New York (ground shipping) yesterday and I was pleasantly surprised with the final product. Had a few things that I would have liked to turn out differently and was wondering what I could do differently to make those things happen.

First of all, there beer had a great light amber color and a very frothy head. Very pleased with both of those aspects.

The taste was almost there. It definitely had the features of an IPA but I felt like it lacked the amount of bitterness I wanted. I also thought it was almost a little flat. I forget the exact amount/ratio of priming sugar but I don't think used too little by any means. I also don't think that experimenting with the amount of priming sugar/solution is the right way to go for my next batch unless I want a bunch of exploding bottles to take care of. One thing I was really nervous about was getting all of the priming solution to mix with the beer before bottling while not stirring to avoid allowing too much oxygen into the beer. To avoid this I added the solution into an empty 5 gal bucket and siphoned the beer into the empty bucket in a "whirlpool" motion.

Another issue I thought I may have had was there was a lot of sediment at the bottom of the bottles. I only looked at a few bottles which may have been the last to be bottled but there was an unusually thick layer of sediment at the bottom. Is that normal? It almost looked like the malt extract I was using didn't completely dissolve during the boil.

Any thoughts? Recommendations for the next batch?

The sediment at the bottom of the bottles is normal and a product of some settling but mostly from the yeast sedimentation after carbonation.

A longer primary will reduce the amount of sediment. I, too, have had some issues with carbing up a "big" pale ale (high ABV and IBUs) on occasion. I suspect I needed a higher attenuating yeast to make it work out.

I usually like to chill my beer for a few days before I drink it. I have heard that the CO2 is in the top of the bottle and the chilling forces the CO2 into the beer. It seems to work. Here is an example. I had an APA that had 7 days in the bottle. I took 3 bottles and put them in the fridge. The next day I tried one and it was under carbed. The next day I popped another one and it was under carbed. Pulled the third bottle out the third day any it had excellent carbonation.

My rule of thumb has always been 5 oz of corn sugar per 5 gallon batch and it has always done the trick.
It does seem that higher gravity beers take 3 to 4 weeks to fully carb.