These are the tools that I use in my studio.

Lathe: Jet 1442.

Sharpening: I have a 2 speed grinder with 60 and 100 grit aluminum oxide wheels. I use a sharpening jig sold through penn state industries (works as well as a wolverine but less expensive). I have a dedicated sharpening jig for my Ellsworth gouge. I also have a flat diamond stone for putting the final edge on tools.

Sanding: On most turnings I power sand using 2" and 3" velcro green cloth backed disc. The cloth backed are worth the extra money and can be cleaned with an abrasive belt cleaner stick. I also use these by hand for small turnings like pens and bottle stoppers.

Finishes: I prefer oil based finishes on most of my turnings and use 3 coat's of Tung Oil (100% pure with japan dryer added). For small turnings I use liquid friction polish. 

Dust Collection and Filtration: I have a ceiling mounted air filter system that uses a disposable furnace filter that I blow out with my air compressor. I built this myself and will email the plans to you if you want to make your own. I bought a used dust collector for $75 and replaced the top bag with a 1 micron unit. I added a dust separator lid mounted on a 30 gallon metal trash can in front of the dust collector and this catches 90% of the wood chips before they get into the dust collector bag.

Carbide Tools: carbide tipped tools are becoming increasingly popular. Since I started using these I find that these are the tools I reach for first. The learning curve on these is very fast. The initial cost can be expensive. I bought my first one and since then I only buy the cutters and make the rest of the tool myself. The Easy Wood tool are excellent made in the USA tools. I buy only their replacement cutters as they are designed for wood.