If the logo(s) is only ever to be used on a website, then any of the graphics programs, such as Photoshop, Illustrator, Corel, Freehand etc. are suitable.
However, if the site owner is ever likely to need printed stationery, (to include the logo), then the best option is Illustrator.
Logos using more than one colour, and designed in Photoshop, can only be printed using a 4 colour process (CMYK). e.g. if the logo is designed using just red & black in Photoshop then it would still need to be reproduced using a mix of CMYK, (Cyan, Magenta, Yellow & Black). This means that all the client's stationery would need to be printed in 4 colours, (expensive!).
This is ok for business cards, but when you factor in such things as letterheads, compliment slips, printed envelopes, NCR forms (Invoices, Credit Notes, Statements) etc. etc. then costs are going to be a major concern.
Illustrator can produce the logo as 2 spot colours, red & black. Spot Colours are explained here: http://www.castleprint.co.uk/spot-process-colours....
This significantly reduces the costs of stationery, especially NCR forms, printed envelopes & continuous stationery (computer forms).
Most professional logos are created in Illustrator for that reason.
Hope this helps.