I3 vs dual core

Dual core Pentiums do not have hyperthreading. i3 processors are still dual core, but have hyperthreading... so they can sometimes handle 4 threads at once. That would be the primary difference.

i5 processors are true quad core, and i7 processors are quad core with hyperthreading.

So for instance if you run Prime95 with a Pentium you will have 2 threads. With an i3 you will have 4.

Easy answer = don't buy Pentiums unless you want a very basic machine, Pentiums are junky otherwise. If you use rather CPU intensive applications, go i3, it handles much better.

Hyper Threading (HT) is useful only if the programs you use are designed to take advantage of it. Games do not make use of HT so if you are building an inexpensive PC for playing games and other basic things like surfing and watching movies, then get a dual core Pentium.