By myself when you are approaching to a new data set you should start to watch to the whole problem. First of all get a distribution for categorical features and mean and standard deviations for each continuous feature. Then:

• Delete features with more than X% missing values;
• Delete categorical features when a particular value gets more then 90-95% of relative frequency;
• Delete continuous features with CV=std/mean<0.1;
• Get a parameter ranking, eg ANOVA for continuous and Chi-square for categorical;
• Get a significant subset of features;

Then I usually split the classification techniques in 2 sets: white box and black box technique. If you need to know 'how the classifier works' you should choose in the first set, eg Decision-Trees or Rules-based classifiers.

If you need to classify new records without building a model should should take a look to eager learner, eg KNN.

After that I think is better to have a threshold between accuracy and speed: Neural Network are a bit slower than SVM.

This is my top five classification technique:

1. Decision Tree;
2. Rule-based classifiers;
3. SMO (SVM);
4. Naive Bayes;
5. Neural Networks.