Best Machine for Sewing thick layers (bags, etc.)

I'm planning on upgrading from my singer 2763. It doesn't have enough ooomph to get through the multiple layers of the bags I make. I have Amy Butler's weekender pattern, but won't even attempt it on my machine. I don't have a huge budget, though.

Can anyone recommend a machine that's powerful, but simple? I don't need a lot of fancy stitches, or anything. Thanks!

I have had a simple Janome travel mate and I have a Janome 4400 and both sew through THICK stuff without crying. MY daughter has a Janome from Handcocks and again, it sews through really thick stuff.... Her is a lower end model.


Ginger

With a size 18 needle, my Brother XL 6452 sews through anything like buttah.    I also have a couple of older machines (both singers) that can do outside fabric+peltex+iron on midweight interfacing+inside fabric..and sew through all the layers for the stitching at the top.  I always use 16 or 18 needles & this seems to work, and the presser feet have an 1/4" lift, so that probably helps, too. 

PS.  I have a Consew, too (I bought at an estate sale)..but, to be honest, I don't really use it that much, unless I'm working with leather or vinyl.