Help with engraving

So I'm pretty new to this but have a good idea of what to do. I've got my hands on a used machine and using Aspire to do my works. However my first issue is the cutting. Using a 1/8 to cut through 6mm mdf and a 0.1mm 30mm to engrave, not in that order, leaves a small edge of the shape that sometimes lifts. I know this is the quality of mdf but am only currently playing with some ideas.
What would be a cheap, lightweight preferably light coloured material to make little shapes from.
Im talking little tress and other Xmas shapes, but want approx a 2mm border around the actual engraved detail.
Will eventually be looking more around 2mm thickness, maybe 3, but can't afford for quality issues like the lifting of the edges.
I imagine ply will splinter too much, what other options are there??
Thanks

You might look into some of the plastic sheet materials, like polycarbonate (Lexan), which machines pretty well without the tear-out you're experiencing with the wood-based products. It's not the cheapest material there is, but you seem to be putting a lot of work into each one of these things, so investing in something that would look more valuable when you're done seems worthwhile. And if you're making small objects, you might be able to find scraps or cut-offs for free, from someone making larger things.

Thanks for the reply, I was hoping to stick to traditional and old fashioned styling, ie just wood, but as it's fine lines, like drawing but obviously shallow engraving, might need to rethink, it's a shame cos everything looks great in mdf but just can't get the quality.
Might need to try a few other options, iyho would 3mm ply give a good finish? I've seen people selling lots of anniversary plaques on fleabay etc but they are usually laser cut, wondered if anyone had e perience similar before laser was affordable