I've never played the game any other way. I literally walked everywhere I went unless I needed to run, on foot of course. It really adds to the immersion when you walk from your car and into a mission marker, try it you'll see. I never went on the notorious "GTA Rampage" because it seemed pointless to me. Why would I want to have a massive shootout with police if I could avoid it? Nothing good ever came of it.
I once tried to drive "normal" by stopping at red lights and whatnot but the a.i. cars reacted like I was in the way since the game is not programmed to be played like that. When it came to weapons, I usually tried to have no more than 3 on Niko at anytime but this is too difficult since he automatically acquires weapons when walking into them, and it's overruled by the fact he pulls them out of thin air anyway. I usually changed Niko's clothes and tried to eat something every few days or so, once again to add to the immersion. Some things I didn't mind like stealing cars when I needed them or street fighting from time to time. It's alot of trouble to play realistically but it makes the game alot better.
I do caution you that if you take this approach, it will take longer to complete the game and you'll have to limit the time you play with frequent breaks. Inevitably, your mind will get bored if you aren't doing something super stimulating and that might lead to you doing a few crazy things, it did for me.
Also, any deaths I may have occurred during gameplay I always just pretended never happened. It is too much trouble to completely reset the game because of one death. I also noticed people on this forum telling you not to steal cars because it would be unrealistic but Niko is a criminal so it's completely realistic. Stealing a car from time to time is okay, just don't go from car to car taking them.
WOW. This is EXACTLY how I play! I like your thinking