The ties you find in the store are typically make out of silk or some imitation silk poly. So it will come as no surprise that those are good options.
In general, you want something with good drape so that you tie hangs nicely. Cutting your tie on bias can help here too.
Personally, I like using different fabrics for ties. Things like denim or corduroy make great ties, while being a bit different from the run-of-the-mill store-bought tie.
Additionally, silk and silk imitation is slippery and tricky to work with. If this your first tie, consider an alternative fabric that is more forgiving.
Just make sure you pick a fabric that does not stretch or lose its shape easily. You want your tie to look sharp, not saggy.
The lining of the tie is the bit that is used at the tip to cover up the back. If you are not sure what I mean, look at the back of the tip of an existing tie. See that rectangular patch of fabric you can see there? That is the tie lining.
Your tie lining will add an extra fabric inside a part of your tie. So it is important to avoid bulk. Go for something thin, even when using a thicker tie fabric.
Make sure your lining drapes at least as good as your tie fabric, so that it doesn’t interfere with the drape of your tie.
When in doubt, go for imitation silk. Do make sure to pick something that is a nice match, or contrast, with your tie fabric.
Your tie interfacing is the skeleton of your tie. It is the part that sits in the middle and that you will only see while constructing your tie.
Tie interfacing can be notoriously hard to get. The best tie interfacing is soft, fuzzy woven lambswool, but I have yet to walk into a fabric store that carries this.
While you can get by with an alternative, like some wool fabric, or flannel, I typically re-use the interfacing from an old tie.
As long as you keep your tie away from scissors and bondage fanatics, your tie interfacing will effortlessly outlast your tie. So look in your wardrobe (or the charity shop/thrift store) for that old tie with the stain on it, and take it apart to salvage the tie interfacing.
As long as the tie you want to make is not wider or longer than the one you are recycling, you have your tie interfacing right there.