If you don’t want to spend a lot on a stick, then the SF4 SE stick is a good option. Easily moddable if you want to upgrade the parts in the future and stock it’s a decent stick.
Between the HFS3 and SE, go with the SE for the reasons Kazujiro gave. However if you want to upgrade with Sanwa/Seimitsu, it would cost ~$25 for the stick and ~$20 for the 6 buttons, leaving you with a ~$85 stick. Or, you could pick up the TE now for $100.
I just got my TE and I love it over the HRAP3. I’ve never used the HFS3 but I’ve checked out the SE in person and it’s very solid feeling. Everything the people above mentioned is true. The only concern is backwards compatibility with PS2 games on the PS3. If you don’t have a BC PS3, get the Madcatz. That’s my OPINION