I just picked up a Ruger 10-22 Takedown model 11112, with the removable flash hider with the intention of getting a suppressor for it.  I don't know squat about suppressors themselves or the processes involved in acquiring one, so I’d appreciate any tips and advice.

I know Surefire makes a new model SF Ryder 22-A and I trust their brand, so unless there is a good reason to go with another brand, that is probably the one I will seek.

From different bits and pieces I’ve picked up on this site I believe I have to file some sort of application with the BATF and pay a $200 fee and wait a long time before actually being able to own a suppressor, but I do not know where to get started.

I assume I first would need to find a place that has the specific suppressor I want to purchase and then then after putting a deposit or maybe even the full purchase price down, they would help me with the rest of the process.

So, if my assumptions above are correct, where is a good place in West Michigan to purchase a suppressor from and is the Surefire Ryder 22-A a good suppressor to start out with?

Being Surefire I’m sure they are priced higher than many others that might be available, but I can’t see spending $200 on a fee to purchase a lower end suppressor.  I’m assuming if I’m going to spend $200 for the permission to own a suppressor that I should buy a top of the line one.

Your assumptions are correct. You must first find a class III dealer who has the specific suppressor you want.  One example in West Michigan is Silver Bullet Firearms. They require a 50% deposit, and will help you with the paperwork.  Another good option is Tigon III Enterprises.  He sells them part-time as he is a practicing veterinary surgeon, but he is very helpful.

The paperwork (called ATF Form 4) is relatively straightforward, but does include the need for a passport photo and fingerprints. The most difficult part however is the law enforcement sign-off.  You must present the paperwork to the chief of police in your county for his signature.  Depending on where you live depends on how easy that will be. Some counties refuse to sign.  If that is your case, you'll have no choice but to find an attorney (more money) and obtain what is called an NFA trust.  This legal document is accepted by the ATF and eliminates the need for a police signature.  There are also several other advantages I'll let you discover should you choose to go down that path.

Yes, this is all very annoying, but it is the price you pay to get that coveted "permission slip" from Uncle Sam.

As for suppressors, I know Surefire is a trusted brand, but they should stick to flashlights.  Their Ryder suppressor is made entirely from aluminum.  The two things I hate about that is the fact that aluminum will eventually wear out faster than other materials, and aluminum cannot be as easily chemically or physically cleaned without damage.  I would strongly recommend you investigate Silencerco's Sparrow suppressor.  It is 100% stainless steel, and is the same price as the Surefire.  As you have mentioned, this is a lifetime purchase.  Choose carefully.

I have acquired two suppressors since they became available.  I have a Silencerco Sparrow, and a Thunderbeast Arms 30P-1.  I very much enjoy both of them and would encourage you not to let the red tape dissuade you.  Suppressors are so much fun.  It is hard to describe the enjoyment of shooting without earplugs, especially with your friends and family, and extra especially with new shooters.

What part of Michigan are you in? We can help direct you to a class III dealer that is close.

Also, what county do you live in? Do you know if you will be able to get a signature from the chief law enforcement officer?

If you live within city limits (as I do, in SE MI), your first stop for a CLEO may be your city's Chief of Police, not the County Sheriff, who would be your likely second choice if your Chief won't sign.

There are low cost "DIY-ish" trusts targeting the NFA market.  Look over in the Armory tab, in the Class Three - General, and - Legal forums.  Another alternative that was commonly used until the "NFA Trust" movement took root a few years ago was the LLC.

As for which suppressor, I'll add that a Titanium suppressor combines lower weight similar to Al with relatively higher strength and chemical resistance, at a cost of course.  But as they say, "Buy once, cry once."

Best of luck with your pursuit.