Enums are a hack for the fact that MySQL didn't have proper referential integrity until recently. In this case, the better answer is probably to put your column in a seperate table which is linked to with a foreign key. You can use a subselect (another thing MySQL only recently got) to get the data back out:

CREATE TABLE payment_types (
    id     int primary key auto_increment, 
    name   blob not null unique
) type = InnoDB;    -- Because InnoDB doesn't suck

CREATE TABLE order (   -- or whatever you call it
    id        int primary key auto_increment, 
    pay_type  int not null, 

    -- other columns

    FOREIGN KEY (pay_type) REFERENCES payment_type (id) 
        ON DELETE RESTRICT
) type = InnoDB;

-- Example insert
INSERT INTO order (pay_type) VALUES (
    (SELECT id FROM payment_type WHERE name = 'VISA')
)
[download]

Yes, there is a performance hit. It's also a much cleaner implementation.

Update: s/FOREGIN/FOREIGN/. Thanks to cLive ;-).