More than likely, yes, the ink will bleed off. After you print your sheet, you'll need to seal the ink. Some people are using Testor's Decal Bonder. I tried it (2-3 coats) and my test decal still bled. I hit my sheet with a couple coats of Testor's Glosscote and as a precaution, after I trimmed out a decal, I hit that again with Glosscote to seal the edges (since trimming the decal could allow water in). That decal worked fine.
Inkjet applies color by applying mixes of Cyan, Magenta, Yellow and Black (CMYK) liquid toner onto the paper. A few of the newer photo inkets add Light Cyan and Light Magenta to the mix to improve the tone of the colors. Inkjet prints don't like water very much if you catch my drift.
Laser printers use dry powder toner and heat to apply color. I think the quality of a laser printer is much better than your average inkjet, but they're also a lot more expensive. However, with a good photo printer (inkjet) you can still get good results with homemade decals.
Alps printers allow you to print white, somthing neither a laser or inkjet can do. The advantage here is, you can print light decals for use on dark finishes. Also, the quality of an Alps is probably better than both inkjet and laser. Don't know much about cost of an Alps or availability, hopefully someone reading this can fill in those blanks for us both.
As for which is best? depends on how many sheets you plan on printing and of course, your budget. A good photo inkjet will run in the $100-$250 range. A laser printer is in the $500-$2500 range.
Now, make sure the decal paper you use is the right kind for your printer. Don't use inkjet paper in a laser printer - you'll get toner on the rollers inside of it and you'll end up wasting a lot of subsequent prints getting rid of it.