I have been using Phusion for years and I am satisfied with it. I usually make two minipreps for each cloning and send one for sequencing, keeping the other one as a back-up in case there is a mutation in the first one, but this is rarely the case. I would advise against using regular Taq except for checking the size of amplicons. As to the hybridization temperature, if using Phusion, I plan the hybridization temperature according to the Tm calculator software provided by Thermo Fisher : https://www.thermofisher.com/fr/fr/home/brands/thermo-scientific/molecular-biology/molecular-biology-learning-center/molecular-biology-resource-library/thermo-scientific-web-tools/tm-calculator.html#. Alternatively, some PCR machines feature theopportunity to program a temperature gradient across the heating block, so your optimal hybridization temperature can be determined experimentally in one experiment

This really depends on how you sequence.  You probably want high fidelity for NGS methods.  But if you just shoot your PCR product off to a Sanger sequencing service, Taq is just fine.  The advantage of using Taq is that if your sequence is "average" in terms of GC content and overall complexity, Taq often works best, and the conditions published in the literature for the most part still refer to Taq.

So what about errors?  The way that works is this:

You can calculate that every product in your typical Taq run has on average 2 errors.  (that's the estimate from Thermofisher trying to peddle higher fidelity enzymes, but we'll believe them for the sake of argument :)  So 2 errors in your product.  You can see thos errors directly if you clone the product.  But if you send it of to Sanger sequencing, you won't:  

The errors are random.  Each happened in a different cycle, in a different place on your molecule.  But Sanger sequencing doesn't examine individual molecules.  You get to see only the "average" sequence.  So if there are 2 errors in a 500 bp molecule, the way that affects the Sanger traces is not by giving false peaks in 2 defined positions;  But by raising the background beneath every peak by (2/500) = 0.4% -- far too little to see or have any effect on automated peak-calling. 

For practical purposes, the fidelity of the Sanger sequencing reaction is going to be the factor limiting your data quality, not the PCR amplification. 

I second that!  Phusion is a very sensitive and high-fidelity enzyme.  I have had successes with it for years.  On of the advantages is that it uses Tm+3° for annealing temperature, which can improve the specificity.  In terms of the Tm calculation for your primers, different companies use different equations, and the result can be drastically different.   In my experience, Invitrogen, Eurofine, and Sigma's equation usually gives higher estimation.  Considering Phusion's "Tm+3°" temperature preference, I stick with idtdna.com's OligoAnalyzer, which typically results in lower estimation.  And this combination worked well in 90% of my PCR adventures.   

Doing a gradient PCR (Run PCR on different annealing tempertures) would be the best way to identify the best PCR temperature. 

Ok  thank you all for your answers, that is really nice from you, I'll try the Phusion, I saw it before and was about to ask advice about it so perfect ! Thanks again

Dear Lola

As far as I know, there is (neither theoretical or practical ) no PCR enzyme which can carry out all the amplification you desire. You have to try a few enzymes to get the required results.