Hi Tim,
to ISS, where we LOVE to spend other people's money,
As Scott and Allan have mentioned, a 10" dob is a sensational first scope.
To answer your questions,
1, A 10" instrument has plenty of aperture grunt for galaxies and nebulae. But there is one thing to be aware of with galaxies and nebulae - you won't see the lovely spiral arms or the wonderful colours like you do in photos. Instead, things through a scope are much more subtle and faint, and require patience and a training of one's eyes to both see more and pick up detail.
With a 10" scope, there are only a handful of galaxies that will begin to reveal their spiral structure. And what you will see is not very pronounced, but more of a tease. Nebulae will show a how lot more structure, and the more time you spend on them, and understanding the forces and structures at play, the more you will see. Nebulae can have tremendous forces at play, but you wouldn't know it as things appear static, but only because of the vast distances involved. Visual astronomy is all about subtlety of detail and keenness of eye.
2, Tracking is certainly not essential. Yes things move across the field of view in a non-motorized instrument, and this movement is faster as the magnification is increased. But one can use a technique called 'drift' where one puts the object to be viewed at the edge of the field of view, or just outside it, and allows the object to drift across the field of view without shaking. Here, wider apparent field of view eyepieces help with the length of time that drift happens.
GO-TO is also not a magic pill. It can be useful but by no means essential. I have various go-to and push to systems available to me at home, but when it comes to my own personal scope time, I only use good old paper charts and star-hop to a target. Push-to systems are a step between push-pull manual moving, and totally automated go-to system. They use electronic encoders to determine the place the scope is pointed to and give a 'countdown' guide to how far to manually move the scope in order to acquire the desired object. These systems are great as after market add-ons to dobs that will be difficult, if not impossible to convert to a go-to instrument without a total overhaul of the scope and mount. When accurately aligned (a process that both push-to and go-to systems require), other than tracking, push-to systems can be faster to use than go-to systems. These push-to systems are better known as Digital Setting Circles.
There are two excellent systems available that are made in Australia,
Argo Navis made by Wildcard Innovations, and
the various Nexus systems by Astro Devices. Both are easy to retro-fit to most instruments. Other systems include Sky Commander and JMI MAX.
3, Filters, like go-to, are not a magic solution, but a damn fine help in the right instance. Astro filters, like all filters, work by transmitting only the required frequencies of light that are of interest to us. Filters for deep sky objects are designed to transmit a very select set of frequencies, and absorb everything else. For this reason they are good for nebulae, but not good for galaxies or stars as these glow across the entire spectrum. Nebulae glow at very exact frequencies.
This following link will take you to a great source of information relating to filters of all types for astro. Understanding what each filter does will help you make the best decision for yourself. One word of caution - don't go overboard with colour filters for the planets. You won't use these very much - really you won't. If you do want to get colour filters, try to limit your choice to two, three, no more than four. The types of features that these filters can show on the planets can actually be surprisingly difficult to see, and require experience and time to make out. Most of these features will not stand out like the proverbial doggie's:
http://www.lumicon.com/pdf/3filterspec_prnt.pdf
If you can before you make a purchase, try to get to a star party, organized by a club or an informal one, and see scopes of all types, and the many different types of accessories actually in use. You don't buy a car without seeing it in the flesh and driving it. Scopes come in many different sizes, capabilities, ease of transport and applications, not just price. If you buy a scope that in the end is too big to store or transport, it doesn't really matter how much of a bargain it is as you just won't use it. The BEST scope is the one that actually gets used.
Happy viewing,
Mental.