How big is "big"? How long is "long"? Best? You're asking a very subjective question. There is IMO probably no "best" if for only the fact that the market is continually cycles back and forth in terms of trending/consolidation and degrees of volatility. Generally speaking for stock indexes I'd say 15min or greater. For individual stocks (which I don't play anymore) it probably depends on the "personality" of the specific issue. When deciding on a time frame I (1) fall back on literally thousands of hours of screen time and (2) create charts of several time frames of the symbol I'm interested in and "eye ball" it to see what looks like about what I'm looking for. Years ago it was probably safe to say that MOST every one was looking at the same few time frames. With the wide range of "time frames" afforded by today's charting packages the possibilities are almost endless.
The higher the time frame the easier you will stick to your plan. When for example derriving signals from the 30 or 60 min whilst others trying to pick tops and bottoms on the 5 and 10 min you have time on your side working into your pocket. You will have less signals but thats the purpose of quality trading in the end - to select the clearest play with enough time to rethink and adjust BEFORE your stop or target is hit. Therewith you also go for the bigger moves and save a lot of commission.