I've posted about how I use the engine for analysis before. Bascially what I do is set the GUI/engine combo to analyse every move once out of book and provide me with the evaluation. I then go through and get rid of anythying that that isn't at least .5 difference between the current and previous move. I also let it think for 30 seconds per move; I have a limit on my GUI to only do time and it seems to me that mostly, the engine gets plenty deep in its analysis, though some early middle game positions that may not be true.
I use that as a starting point to try and analyze those positions/moves to see if I can see a better continuation. If I find something I like better I'll check it against the engine and see how my thought process compares to what it likes. If I didn't see something obviously better, I also check the engine and see if I can figure out why the top lines it gives are actually better. In the absence of obvious tactical or forcing lines, I often find that doesn't help a whole lot and I will add a variation if the score differnce is significant, for further study.
I will agree, I don't think the choice in engine matters a whole lot for amateur players. I currently only use free engines (Houdini 1.5a right now) and a free GUI for the analysis.
The database/tablebase variable? The database usually isn't used by the engine, though it does use it's opening book and that, as expected, is only valuable in the opening. Tablebases will help in the endgame evaluation but only when the engine starts evaluating positions with the requisite number of pieces (depends on how many pieces your tablebase covers).
I do not play against chess engines, I use them for post-game analysis of my own games, mostly my losses, as a learning tool. I use Fritz 13 as a GUI and Stockfish or Houdini 1.5a or the Fritz 13 engine, depending on what I want to analyze - it doesn't matter much, I suspect.
In setting up the engine for analysis, there are a number of parameters available to me, which has caused me to rethink how I use my engines and settings, and the results of the analysis. Those parameters are settings for depth of analysis, time per game, and/or time per move.
As an "average" chess player (whatever that means), I do not often think more than 4-5 moves in advance, especially in complex positions. So what is the advantge of sending an engine off 30 plies down the road to determine the best move for me in that position? Since I (and most other players) are incapable of seeing even a dozen moves ahead, why push the analysis so far beyond the point where it has any practical value to humans? And to that end, does it really matter which engine is 10 Elo points stronger than another? Not unless one engine demonstrates a weakness in one aspect of the game such as a weak endgame, and we have seen examples where an engine missed an obvious "win" or draw. Additionally, during recent live chess broadcasts such as the Candidates tournament, the commentators (Nigel Short, et.al.) disagreed with engine analysis in several positions and we saw the scores changing as we followed Short's analysis.
There is also the database/tablebase variable. Does changing the database or tablebase used change the evaluation scores? I would expect so.
So what I do in my own study is to use more than one engine in a tricky position and compare them. I also pull back the analysis depth and compare the results of, say, 10 plies vs. 30 plies and see if it changes the recommended line. Seldom does it matter to the engines, so it shouldn't matter to me playing and understanding at half their strength. Using excessive analytical depth is not all that different from trying to read a book for grandmasters that is far over my understanding level.
So do some playing around if your GUI allows you to set ply depth and analysis time per move and see if you aren't a victim of overkill. Trying to follow an alternate line leading to a 0.05 theoretical advantage in 30 plies may be worthless in the mistakes we make trying to get there.