What type of rum to use when making vanilla extract?
I've been making rum-based vanilla extract successfully at home for years. Here are my recommendations. Your basic ingredients are 80 proof rum, sugar and vanilla beans. At the recommended proportions, the rum and sugar are plenty effective preservatives. 

You can use either light or dark rum, but it should be a good "call" 80 proof rum and not a bargain bottom shelf rum. I most often use Ron Rico. If you use a golden rum, your extract will have a warmer taste suitable for spicy treats such as pumpkin pie or spice cookies. If you use a silver rum, your vanilla will have a purer taste suitable for whipped cream or custard sauces. I get rum that is bottled in glass, because I think plastic imparts an off flavor. 

Your basic recipe will use a fifth less about a 1/2 cup of rum, four vanilla beans and 1/2 cup of organic sugar. We'll go through that first, and then talk about variations. 

Place your vanilla beans on a clean, flat cutting surface. Using a small, sharp knife, cut them first in 1/2 crosswise at the middle. Then take each 1/2 bean and insert the knife tip just 1/2 to an inch below the uncut end and carefully slice lengthwise to the send. Repeat this process gently and carefully on each piece unti each piece  has four lengthwise quarters attached at the uncut end. Some recipes will tell you to scrape some or all of the paste out of the beans, but this is not necessary. The simply split beans will infuse the rum just fine. 

Pour out about a cup of rum from your fifth and set aside. Put your sliced vanilla beans into the rum. Use a funnel to add 1/2 cup of organic sugar. Use the reserved rum you set aside to top the bottle back up. Recap the bottle and give it about 20 shakes to encourage the sugar to dissolve. Set aside in a dark cabinet or pantry. Take it out and give it a few shakes every week or so. Your vanilla will be usable but not fully extracted in about two months. It will continue to strengthen in flavor out to about 6 months of age. 

Once you are satisfied with your extract, you can decant some and bottle it up in smaller bottles. It's a very popular gift for bakers.

Once you have tried vanilla extract made this way, you will never want to go back to store-bought. The difference is indescribable. 

You can vary the type of rum you use, silver or gold, and you can vary the sugar. I mostly stick with light organic sugar, because I think the taste is better. I like the combination of dark rum and brown organic sugar very well. You can also increase the sugar up to about 2/3 cup in a fifth bottle, but I wouldn't go above that. Sugar gives the extract more body and mellows the flavor.

Check out Wikipedia to learn more about the various kinds of vanilla beans available. I use the organic ones from my food coop, but different kinds can be ordered online or found at specialty food stores. 

A number of cooking blogs have instructions on making extracts or tinctures of other spices. There is no reason not to create combination flavors.