Hi there. Any machine that could do this will not be cheaper than a Cricut - at least up front. Machines like the Gazelle, Silhouette, and Black Cat are all computer driven and come with software so you can cut any font, any image, etc. They are all more expensive than the Cricut, however for the Cricut you have to keep buying cartridges to get more images and that's where it gets really expensive.
To my knowledge (although I could be wrong), none of these machines will scan, you'll have to scan the images separately and import them to your cutting software. Also you'll have to do a little work in the software to make a scanned image cuttable, it's not an automatic thing.
I have a Gazelle and love it to pieces, WAY better than a Cricut imo.
I have the silhouette sd and can scan something on my regular scanner, open it in the free silhouette software and trace and cut with just a few clicks.
Yeah, depending on the image it can be really fast on my Gazelle software too. Sometimes I create cutting files from photos, very low resolution clip art, or images that are just messy for one reason or another - these take more tweaking, sometimes a lot.
Micheal's has the Slice machines on clearance for $40 and design cards for $10... you may want to look into this. But, search on here to see what people think about it. I have found people love them or they hate them, strong feelings both ways. Good Luck!!! Let us know what you end up with!