I don't want to restate what has already been stated but I have a few things to add... which may turn into a longer post but I'll try to be succinct. (Not my strongest skill I'll admit...)
First off, I'm not the best to give tracking advice but I can give some feedback on mixing and mastering so I'll just skip the recording part. Onto mixing...
As far as your question of "What's the cheat?" well... there isn't one really. It just takes hard work and practice. If you're looking at a quick turn around time for this project and you don't know what you're doing from an engineering standpoint, you might consider hiring a mix engineer that can do the job for you. If you do know what you're doing or you're up for the challenge of learning then you need to understand your tools at least well enough to get a result you are satisfied with. If you are truly lusting after the very best production you can get, you will need time and practice, and adequate gear. You can mix fully "in the box" (on a computer) without using outboard processing if you choose to do it this way. This way is generally easier on your wallet, but there are advantages and disadvantages to each route. Logic will handle all of that for you. You might look into VST or AU plug-ins for effects that are not native to Logic, though Logic has some very good plug-ins that come with it. The biggest "cheat" I can think of is: good gear often helps good sound, but if you are mixing a shitty recording, it's going to come out sounding like you mixed a shitty recording. If you are getting to a point where your gear is holding you back, don't be afraid to admit it to yourself, but conversely, don't be fooled into thinking higher end gear will make you a wizard.
From a technical standpoint, what you need to know could be stated in an entire book (which you may benefit from reading a good one) but for now you should learn the basics of your processing units: EQ, compression, reverb etc. You should also get a coherent understanding of proper gain staging and I think that cannot be stated enough. It's often overlooked and it's very important and can make a huge difference in the quality of your productions, not to mention understanding gain staging is invaluable to building a solid foundation to learn production on. Again, terms you would need to know could be talked about in a book. Look into all your effects. Learn those terms, and learn the parameters and what they do. Just go through and find anything you have questions about and Google it. There's a ton of information out there. Again, a book could help put all this information in one easily digestible place so it may be worth finding a book you think will do well for you.
You will want proper monitoring. You CAN mix on headphones but I wouldn't particularly recommend it. Not everyone will agree with me on that but it's truly how I feel. Unless you want to spend close to $1k on headphones, you're going to make some compromises along the way. Even with a very expensive set of headphones there are still advantages to classic monitoring. Having said that, using headphones in conjunction with monitors for referencing can be a very good practice. For monitors, find something that is revealing as has been stated above. A set of monitors that shows all the faults of your mix is much more valuable to you as a mix engineer than a pair of monitors that flatter your mix. This is why NS-10's are extremely popular in high end studios. On the note of monitoring it is well worth mentioning that acoustic treatment is a valuable addition to any studio. I, personally, am of the belief that you can mix in any room given time to get used to it but you will constantly be fighting an uphill battle until you are used to your room and even then you will need to learn the value of referencing professional tracks. Basically, room treatment can make your life easier.
As far as your comment that you want to get the best result with minimal effort... a very understandable sentiment, however, don't expect to get away with making something very polished with very little effort. It just doesn't work that way. Mix engineers work just as hard as musicians and there is just as much time and dedication put into the art of mixing as there is put into the art of playing and performing. Just learn your tools and learn to enjoy the process. That's all I'll say about mixing for now.
To address your very last question about finding the same volume for all tracks: That is the job of the mastering engineer. Mastering is a whole other can of worms. You could get by with some mastering software, as stated already above, something like Ozone or T Racks or something. But you must understand that mastering engineers have a different perspective than a mix engineer in some ways. There is a lot of overlap but what you are looking to get out of the process is different in some subtle and some not so subtle ways. Basically, mastering aims to bring your tracks to commercial loudness while also preserving dynamics and often there are other small finishing touches added such as harmonic saturation or stereo widening etc. If you don't want to learn this or do it yourself, hire a mastering engineer. It will be well worth it if you are not confident in your ability to master. It also can give you a fresh perspective on a track which can be invaluable at that stage in the process.
I know I've said a lot here and I don't mean to intimidate you I just want to be clear that if what you are after is truly commercial level mixes then there is a good body of stuff you need to know. The people cranking out commercial mixes are very skilled at what they do and have many tricks up their sleeves. Some of it is very simple and subtle, some of it is very technical and heady. You can choose where you want to go once you have everything recorded but like somebody above stated, what you put in is what you get out. Do your best to make your best mixes and put a lot of love into them and you will be rewarded. It's a process just like any other art form and the more you do it the better you will become.
You sound like a skilled musician and I am excited for you to learn this stuff. I'm sure you could play circles around me on an instrument and I have a ton of respect for people who can do it all so it's a very worthwhile step to take in my opinion. I, myself, am a production geek but I find great pleasure in polishing music and getting creative with audio processing because I find it to be very rewarding. Hopefully you will feel the same. Good luck!