Problems with front derailleur shifting on an inexpensive bike I bought a cheapish bike (Nakamura) couple of years ago, and it generally serves me well. Main problem that I have is that shifting gears, especially front gears often gets out of tune. After only a couple of rides it stops being smooth, and than I soon start having real problems while trying to shift gears (e.g when I shift 1->2 it gets stuck on 1, then i push to 3, and back to 2 and then it clicks, or similar scenarios. At one point before tuning, just trying to switch to 1 meant automatic chain falling from cogs). I tried tuning it myself, and had it tuned at LBS, but results are the same.

Question is, I guess, what can I do about it? Should I buy new derailleur? Maybe cables are bad? Bike is 3x7 and all the new stuff is 3x(8, 9, 10) would buying 3x8 be a problem? What if I go nuts and spend money on entire new power-train (front/rear, cogs/dereilleurs) which would probably be only slightly less that I paid for entire bike? Would it make sense?

Also worth mentioning is that I don't ride a bike that much. In last couple of years, I've barely rode 1000km,and so far I haven't change any part on it, or done any maintenance aside from cleaning/lubing, and derailleur tuning.
I'm sure you're a better judge of how effective your LBS employees are than people on an Internet forum, but in my experience it isn't uncommon to find some LBS employees are not very enthusiastic about working on bikes they view unfavorably for whatever reason: too old, too inexpensive, and so forth. Some think that working on an inexpensive bike is like polishing a turd, and I have run into more than a few who view it that way.

If the bicycle is similar to this one, I would encourage you to check out some YouTube videos regarding derailleur tuning:

Tuning a front derailleur
Tuning a rear derailleur