I've seen and used tons of products over the years. Cleaning is first. If you have gray or almost black teak, a two part teak cleaner is like magic to bring it back to a nice honey color. As mentioned, it is aggressive and so sanding may be required to get the teak surface nice and smooth. Do not use this type of cleaner on a veneer.
Exterior: At the very least you can oil the exterior teak. But, it is subject to evaporation and has to be applied regularly for a good look. I have found digging deeper into your pockets for a more expensive teak oil pays off in longevity.
Varnish is considered to be the most luxurious look, but it also is the most arduous to apply. Epifanes makes a gloss varnish formulated for teak and that is what I have used with great success. You must clean the teak first and sand, if needed, and then follow the instructions implicitly (easy to do) for proper adhesion. And, to achieve that super finish, you have to keep applying many, many coats of varnish to build it up. There is a window where you need not sand between coats. Read the instructions.
Teak has natural oils in it and that is why it is such a good wood for boating use. Besides the Epifanes, there are other cheaper varnishes to use, but most require proper sealing of the teak for good adhesion that lasts. A refresher coat should be applied at least once a year -maybe two. I like Epifanes. You should understand that varnishes that have UV inhibitors in them are not for life. The UV inhibitor feature doesn't last indefinitely and for that reason, it is good to apply refresher coats. Of course then you need to sand lightly. There are tricks to creating super nice varnish effects of which I will mention a few. You should read up on this if you want the best results. First of all, you should pour the varnish through a paint strainer to keep the chunks out. Next, use a good, clean varnish brush. Next, use a second cup to rim off the excess varnish on the brush rather than rimming it back into the strained varnish pot. You will introduce bubbles if you do.
Sikkens Cetol is an easy to use product and they have several formulations from which to choose. Their original had an undesirable orange color that most people hate. I find their Natural Teak formula to be the best for matching what teak is what is supposed to look. It is imperatave that you clean (and sand) the surface before applying. You need a minimum of 3 coats. One per day and all a three should be applied within a 2 week period (I think I recall the instructions read) so that sanding between coats is not necessary. It produces a nice matt finish and if you want glossy, then you apply the gloss formula over the 3 coats that you started out with.
Interior: I have one boat that has a fully varnished inside teak woodwork where Epifanes satin finish us used, rather than glossy. But, depending on what you have, you can oil it, or apply another sealer, but you have to be aware of compatibility. Many new boats come with unvarnished veneer bulkheads, etc. and if that is the case, choose what you like or choose based on the finish you wish to see. I have another boat that I want to refinish the interior and I have no idea what it has now. It is not glossy and it appears to be more than oil. I'll figure something out to make it look better.