Most decent RAW converters (including LR) are non-destructive. The original RAW file is not changed in any way. The edits you do in the converter - colour balance, tonal corrections, etc - are stored in the database and/or in separate sidecar files alongside the RAW file. So for each image you'll have the (unchanged) RAW file plus an extra file (.XMP in the case of LR, .bib with Bibble, etc) which contains details of all the editing you've done.
That means you can move the lot to another computer simply by copying the RAW files together with the corresponding sidecar files, and the same software on the second machine will recognise all the changes you've already made.
With LR you can let it do its own thing with regard to file locations, or you can upload your RAW files to a directory of your choice and set LR to 'Reference files in original location'. That way there will be no duplicate RAW files created, although LR will still create a fairly large database containing all the keyword, tag and editing data, whether or not you tell it to create the .XMP sidecars as well (which you should, IMO).
The editing you do on LR or any RAW converter can be as little or as much as you want, within the limitations of the software. It's a good idea to do tonal and colour corrections in the RAW converter before you create the TIFF or JPEG files, because the quality should be maximised that way. For the very best quality you then convert to 16-bit TIFF and carry out any further editing in your favourite software (Photoshop, PSP or whatever). The drawback here is that 16-bit TIFF files are huge (10 MP image gives 60 MB file
).
One day we may see LR develop into a genuine all-in-one application, which I believe was the original paradigm and is why 'Export' is (or was on earlier versions) almost an afterthought. Adobe seriously believed that you would be able to do everything non-destructively within LR and would never need to convert to TIFF or JPEG. They've a long way to go yet before LR replicates all the functions of PS/PSP, and the nearest there is to an all-in-one RAW convert + editor right now is probably Bibble.