I'd like to buy a Pilot pen, but not sure of the exact model name, possibly Elite or just a "pocket pen."

It sounds like these came in lots of varieties, so here are the features I'd prefer:
14k fine point nib
converter
light-weight
something with color or barrel design (maybe pink/floral?)

If you don't have your heart set on Pilot, Sailor and Platinum also produced similar pens. Sometimes referred to as long-short, since when posted the pen is full size (long) and when capped it becomes compact enough to sit comfortably in your pocket (short).

I have a Sailor in pink that I got from a seller named sakura_zeppelin on fleabay. Sakura_zeppelin has the plain pink for sale right now; item # 370024238692. I've seen them offered by other sellers such as; engeika and possibly kamakura_pens

If you are looking for a short-long, you might have a hard time with the converter requirement. The barrels are too short.

Some of the Pilot's take a converter just fine. Mine does. There are several e-bay sellers that always have these pens. jp_pens and sakura_zeppelin often have them. But if you're not set on a converter, as someone mentioned above the Platinum and Sailor long/shorts are equally satisfying.

I am also planning to buy a Pilot pocket pen, as companion to my Platinum and Sailor pocket pens. If you are not set on Pilot, the Platinum plain black model seems to be more available, and often less expensive. I can't really tell a difference in writing quality between my Sailor and Platinum. Bot have F nibs, and both are extremely smooth and reliable.

Go for the Pilot. I used mine just a short while ago (it has a a converter) and it was marvelous. I love the way the long hood slips on the short body when I post it. Mine has a Fine nib (14k) and even with the relatively small converter, the ink seemed to last forever. A converter just gives you more choices of ink. I used Noodler's Burgundy with much success. They are great writers!

I purchased the pen from Sakura Zeppelin and had a good experience with him. Engeika and Kamakura Pens are great to deal with too.

Good luck! You'll enjoy the pen!

Erick