I'm assuming this is normal...
 

When I was test driving Minis (03 automatics), I noticed when I stepped on the gas that it was sluggish for a second or so, then the power kicked in and she went. Now that I test drove & ultimately purchased my Mini, I noticed the same thing. I am assuming this is how they are made to run since every auto I test drove (03s and an 05) ran this way. Is this normal? Is there any way to get rid of the initial hesitation from stepping on the gas?

I've also been toying around with the idea of improving the performance of the car (exhaust, intake, etc.) but have no idea where to begin. I know very little about the workings of a car...I just like driving them. Money is extremely limited too so does anyone have any suggestions on what I can do to boost performance a bit?

Thanks in advance!

I've never driven an auto and can't comment on it.
I know on the manual tranny the improved gearing with the 05s helped greatly.

As to improving performance: need more info on your car specs. Most importantly, is this an "S" model?
If so, you'll soon see from reading through here that the best bang for your buck is a reduction pulley for the supercharger.

This is normal. Something about the chains in the CVT taking up slack-the SA at mini told me. It's really bad in reverse.

Thanks for the replies. Eager, this is not an S model. It's a base.

Marshall, thanks for the confirmation this is normal. As I stated before, I thought it was since all of the Minis I test drove did this. So I wasn't/am not very concerned about it. Just something to get used to.

This is normal. Cars with small engines and an auto transmission usually behaves that way. That's why I got the manual transmission, made a noticeable difference.

Well if it is a normal aspirated i would say; normal

Not to mention the car is drive by wire throttle, and while you can improve throttle response you can't eliminate it. In my car I've reduced the delay to barely noticeable, but it's still there. Curse of the car.

My and my neighbor's '05s are like that. Apparently it takes a second for the link belt in the CVT to adjust to what you want it to do, then like you said, it'll take off! You'll get used to it, it's a blast, very unique. Have you tried the Sport and Manual shift modes? On the subject of mods, my MINI doesn't have a whole lot yet (mods are addicting), but the very first thing I did was install M7 strut tower braces because of mushrooming issues I found on NAM. (The NAM search button is great for finding information on all of the MINI subjects you're interested in.)