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In either case, more and longer reads are better as you can imagine. With an overlap graph (also called overlap layout consensus algorithm or overlap layout algorithm) your assembly grows much more effectively with longer reads and there are few parameters you can tweak. With a de Bruijn approach, obviously your choice of k can have a strong impact on your assembly.
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k-mer distributions inherent in select genomes
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Some example assembly statistics
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Many (many) assemblers are available. A list of assemblers can be found here.
We'll take a look at Velvet. - it's a fast and easy to use de Bruijn assembler.