My suggestion is simple, and it's one echoed by many computer security researchers. All computerized voting machines need a paper audit trail. Build any computerized machine you want. Have it work any way you want. The voter votes on it, and when he's done the machine prints out a paper receipt, much like an ATM does. The receipt is the voter's real ballot. He looks it over, and then drops it into a ballot box. The ballot box contains the official votes, which are used for any recount. The voting machine has the quick initial tally.

This system isn't perfect, and doesn't address many security issues surrounding voting. It's still possible to deny individuals the right to vote, stuff machines and ballot boxes with pre-cast votes, lose machines and ballot boxes, intimidate voters, etc. Computerized machines don't make voting completely secure, but machines with paper audit trails prevent all sorts of new avenues of error and fraud.