Thanks for the thoughtful reply. I wish I could give you an easy "just buy an XYZ and you'll sound like Abbey Road" but it just doesn't work that way.
I'll revise my previous response to say that the things you need to work on are the acoustics of your recording and mixing environment...and your personal level of skill. The latter is something that can only come with experience and practice.
You mention EQ, compression and reverb. All three are tools very commonly used on professional mixes but there's no single setting or piece of advice that can substitute for just trying things. EQ, for example, is something that's different every time. There are a couple of main functions: first, to simply correct things in the frequency response of your recordings that aren't as good as you want and, second, to help one track of your recording "play nicely" with other tracks. The best recordings (good mic suiting the material in a good acoustic) need little or no EQ. Other times, you're working like mad to save things. Either way, it's a case-by-case sort of thing using your ears.
Compression is also commonly used on recordings. At it's simplest, it's simply an automatic way of evening out the loud and quiet bits of a recording to make mixing easier. However, on some things, often electric guitar, compression can become an audible effect in it's own right. Compression takes some time--and quite a learning curve--to understand and get right. However, once you do, it's an extremely useful tool. Have a read (or three) through these
RANE NOTES about dynamics processing--and experiment with your own recordings as you go.
Reverb? Yeah, it can help a lot of things but beware the temptation to use it too much. It's not a magic bullet that fixes everything--at worst it just covers up the bad bits. However, used properly, it gives your recordings a sense of space, especially when you work in a fairly dead environment.
If you're happy with your room then that's a good start. Getting things just basically dead then adding electronic reverb later is a pretty common technique--one I use myself. However, this could also be a big part of the difference between what you perceive as "professional" as opposed to "home". The most popular studios aren't just dead; rather they are designed to have pleasant sounding characteristics. On corner might sound good on acoustic guitar; another might be good for vocals and so on. However, this is hard to emulate at home without lots of money so "dead" is likely the way to go for you.
Now, the good news: your computer and your drivers don't affect sound quality (other than that, if really badly wrong, your recordings will be full of dropouts and glitches). Similarly, the differences between your mic and a $10,000 one are far more subtle than you might think. Where there IS a difference is that a pro studio has a cupboard full of mics and pulls out different ones depending on what they will be recording. The NT1A is a good all-rounder though and, rather than replacing it, I'd just use it until you reach the stage where you know what changes you want in the sound--warmer, crisper, more mid range detail, etc. and choose a second mic that gives you the desired characteristics. You'll find that gear acquisition syndrome kicks in and you may end up with a mic cupboard as big as Moresound's!
I guess a last thing to remember is your monitoring set up. It's hard to make your recordings sound professional if you don't have the resources to actually know how they sound in the first place. However, I think you're doing the right things in the first place--do a mix then play it back on all sorts of different systems, comparing it to commercial recordings. Mentally note what changes you want--more bass, less bass, more detail in the mids, whatever--and do another mix before repeating the testing. All this is much easier with a good set of monitor speakers but, even with the best, there's still a learning curve. This is also another place where acoustics come into it, by the way. Lack of treatment in your mixing room can quite drastically affect what you think you hear.
Anyway, sorry I can't give you a "buy a Neumann mic and a Drawmer compressor and all will be great" type of answer. It really is just a matter of plugging away at it and learning what your tools will do and when to use them. Your initial set up is good enough that I wouldn't be running out and spending more money just now. Use what you have until you can actually hear what you with to change for yourself.
Happy recording!