Should I have Lasik or rhinoplasty first and how long should I wait to do the second procedure?

Hello.
Great question. There is not set orderer your desired procedures. However, I will suggest discussing this with you surgeon for his post op recommendations. Every surgeons different post op protocols. 

Although you can wear contact lenses after rhinoplasty surgery, there is a distinct advantage if you do not have to use any help with eyesight. I could see that as an advantage for having Lasik first. 
For the interval, I think you need to ask your eye specialist if you choose this sequence. It is not likely to be longer than 3 months and could be a lot shorter. 

If you decide to have rhinoplasty first, count on the fact that some eye surgeons request patients to use glasses for a few days after surgery. This means a minimum of one month but better six weeks from rhinoplasty. Following rhinoplasty you should ideally wear contacts for the first month. 

First, the nose. Besides the small hump on the dorsum, your nose has a couple other features to recognize and address. Your tip is strong in its forward projection from your face. The tip can be brought back closer to your face. We call that "de-projecting" the tip. 
Then, when a tip is de-projected, it makes the nose *look* longer, as if the tip had drooped, so it's rather important to elevate the tip some, at he same time as de-projecting it.
Also, when a bump is taken off the dorsum, that also has the tendency of making a nose look longer.
You have the kind of nose where, if your surgeon doesn't recognize and address all of the areas I mentioned, your nose could look worse, and bother you more. If only the bump is removed, the nose might look bigger, because of the projection and low position of the tip. If the projection is brought back and the bump is removed and the tip is not elevated, your nose could look unnaturally long.
How *much* to elevate the tip, or deproject the nose? We figure that out with morphs, well before surgery. I'd love for you to see some excellent professionally-designed morphs of what could possibly be done with your nose. Morphs could also help you identify what's bothering you, and help you set a goal for the rhinoplasty that's accurate for your tastes. (Side note: in my opinion, morphs should always be done by the surgeon, or he should direct an assistant as she makes the morphs. Morphs should be made with a constant eye to what actually *can* be done in surgery, for that particular nose, and only the surgeon has that information and judgment. Another aside: I also recommend that you not show morphs made by one surgeon to a different surgeon. If a surgeon makes his *own* morphs, you get to see whether he understands the important issues of your nose, and how your nose should be changed. But if you show the surgeon someone else's morphs, and he says "Of course I can make your nose look like that," then you don't really know if he fully understands, or even recognizes, the important changes shown in those morphs. And you don't know if he can make those changes during surgery.)Then, the chin. You are a good candidate for a small-ish chin implant. In a previous post of yours, you showed a chin augmentation morph, where the chin was really way too big in the after photo.Even though your chin is "weak" in its forward projection, it's tall in its *vertical* dimension, the vertical distance from where your lips meet to the bottom of your chin. When the chin is tall, we need to be careful in how far *forward* to bring the chin, lest it look too long. You want your chin to look balanced with the nose and face, not something that draws its own attention.
Remember that rhinoplasty, in particular, is an exquisitely difficult operation to get right, and you should only have surgery if you are able to make yourself very confident in your surgeon's skills. The changes that your nose needs require advanced techniques, and skill that most plastic surgeons don't possess with expertise. For most noses, it's much better to not have surgery than to have inexpertly-performed surgery. Read my essay on how to stay out of trouble while selecting a rhinoplasty surgeon. And it also discusses how to take photos that are best for online evaluations.
Your nose is also a perfect example of why computer imaging is mandatory in rhinoplasty. You need to know exactly what the surgeon is planning to accomplish -- what features he thinks he can change, and by how much he thinks he can change them. I always email morphs to my online rhinoplasty consultations. When you see the surgeon's goals in the morphs, you'll know whether he has an eye for an attractive nose, and whether he shares your opinion of what constitutes an attractive nose. You'll also know whether the changes he proposes are large enough to be meaningful to you, and whether he understands your wishes enough to address all of your priorities. How would you ever get that figured out without the morphs?Finally, the lasik. Remember, you asked. I wouldn't do it at all, for a million reasons. If you only have a refractive error, and the point of the operation would be to get rid of your glasses, find an ophthalmologist who doesn't do lasik, and give him/her a chance to talk you out of it. It's not the carefree complication-less procedure that it's marketed to be.