I need to use M13mp18 (single strand), but I would like to produce it starting from bacteria. Can you suggest which is the best bacterial cell to use in cases? Otherwise, is there any company that sell bacterial cell infected with M13mp18?
Any F+ strain will do. Back in the day we used JM101.
You need either to infect an exponentially growing culture with a suspension of M13mp18 phage, or to transform DNA of its RF form (probably even ssDNA will do).
M13 infects only F+ bacteria (strains carrying the F episome), which MG1655 is not. See the Wikipedia article you reference for details.
One could certainly electroporate the RF form of M13mp18 into MG1655 and select phage-producing clones to be later expanded and cultured, but how that selection would proceed I don't know, as there are no antibiotic selection markers in M13mp18 and alfa complementation is no use in Lac+ strains such as MG1655.
It is easier (and common practice) to simply use an F+ strain (JM101, XL-1Blue, DH5alfa F', SURE, etc).