In fact you should do BOTH! State the minimum required and state the recommended version. The latter should have been thoroughly tested.

Having a lowest supported and a recommended might have a lot of added value to a module. Say that the newest/hippest module adds a feature that can speed up you code by a factor 10, it is worth supporting that with a fallback to the old code if the newest feature is not available.

You META.yml might then have a section similar to:

requires:
    perl:                5.008001
    DBI:                 1.628
    DBD::File:           0.42
    SQL::Statement:      1.405
    Text::CSV_XS:        1.01
recommends:
    DBI:                 1.636
    DBD::File:           0.44
    SQL::Statement:      1.412
    Text::CSV_XS:        1.31
configure_requires:
    ExtUtils::MakeMaker: 0
    DBI:                 1.628
build_requires:
    Config:              0
test_requires:
    Test::Harness:       0
    Test::More:          0.90
    Encode:              0
    Cwd:                 0
    charnames:           0
test_recommends:
    Test::More:          1.302085
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