I at least try to sew with it first, if for no other reason than to figure out if it needs anything other than a cleaning, and if it's worth the effort.
After that, I start taking it apart. All of it. Some parts will just get a wipe down, others scrubbed/polished. I'll take the motor off and at least peek inside - remove lint, dust or "whatever" might lurk in there, if it needs more attention (haven't had one yet) I'll tackle that as well (I have a friend that has a business rebuilding elec motors - he's been a great help teaching me "stuff"). Ditto for the foot pedal, take it apart, clean. As I'm disassembling I assess each part to see if it needs to be replaced/repaired or just cleaned/polished. Replace wiring if needed. I keep all the parts in marked baggies and I take a lot of photo's so I know how to put it all back together.
Once I have the machine stripped of parts that can be stripped, I then go to work on the japan of the machine.
If old dirt/oil is on it I'll scrub with an old t-shirt and sewing machine oil. If it's really bad, I might use a bit of detergent (after testing) but I'm always careful to rinse with clean water then rub with sewing machine oil when I'm done with that area. Once I'm happy with removal of dirt/oil from the machine I'll buff off all extra oil using a clean dry old t-shirt. Last step is to apply a carnuba wax polish. After that ... reassemble and give it a test drive. If all is well it goes into it's cabinet!!
I haven't (yet) needed to do the "french polish" method on any of the machines that I've worked on. I have two that will need it ... just haven't gotten to them yet.
I also haven't yet tackled a crinkle finish ... I have one but I've not touched it yet. I suspect (but will investigate first) that I will be using a different method ... soap vs sewing machine oil is my suspicion.
I have purchased one machine that someone else had cleaned and finished, my W&W 8. Now that I know a little more, I would say I paid too much, but at the time I was happy with the deal and I don't regret getting it. I'll be a little wiser if I ever purchase a 'finished' machine again, but it will have to be a pretty special machine.
As for selling ... I like working on the machines, it's fun. I only expect to get what I paid for them including any parts I had to purchase, and shipping and packaging that I might have to do (averaging them all out - I paid ninety nine cents for one machine, and up to $100 for another ... so average them both to $50). I work on machines only when I have the time and feel inclined to work on them ... so really not all that often. I don't want to be known as "the lady that fixes and sells sewing machines". I kinda just want to have fun and be able to get back the $$ I spent (not counting supplies, I consider those as part of my hobby expense).
I also concentrate on certain types of machines. I don't like the zig-zag machines and I don't like machines that have a 'modern' shape to them like Rocketeers, 301's, etc. I like the "Singer swoop" silhouette ... it appeals to me, as well as some of the older funkier shapes ... like an old Wilcox & Gibbs, or a Grover & Baker.