How to convert AVI file to another format that is compatible with Premiere?

All of my movie files are in AVI format and whenever I convert them to MOV in order to edit on Premiere my file will be up to 2 GB in size even though the original size is 700 MB. My problem is that whenever that happens, it hurts the available space of my laptop and it sometimes discourages me to edit on Premiere. I hope to find an answer that when I'll convert to MOV (or any other format that is compatible with Premiere), the file size should not exceed 700 MB or so and still has the same quality as the original.

Here are the settings that I normally use:

(When exporting to a QuickTime Movie)

Video Settings:
Compression Type - H.264
Motion Frame Rate - Current fps
Motion Key Frames - Every 24 frames
Frame Reordering checked
Data Rate - Automatic
Compressor Quality - High
Compressor Encoding - Best Quality (Multi-pass)

Sound:
No sound (unchecked) (The file will be 5 GB when I add sound)

Frame Size:
540 x 304 (16:9)

Interlaced Scaling checked

Field Dominance:
Upper Field First

I'd like to change any of these if necessary to have a best quality 700 MB (or so) movie file. Are there any formats that I could use other than MOV that will not eat up my available space? If so, what are they? I'm not really familiar with the formats. I'm only familiar with MOV and AVI in terms of converting.

Any help would be gratefully appreciated. If you can point out what I'm doing wrong, please explain and I'd be thankful as long as you can teach me how to make it right.

Yes, but I don't have QuickTime Pro, so I can't use the Save option. Is there any other way in order to do this?

I'm using another media converter. I guess I never thought about using QTPro earlier. Anyways, thanks to jackerin and Keebler for the help!