Amazon seems to do a good job shipping to Mexico, but always check prices locally first. Many times the shipping and customs fees offset any savings of buying on-line or through a US retailer. Remember also IVA (VAT) of 16% will be charged on any (legally) imported goods.
Once you are settled, you'll find everything you need in Mexico; with rare exceptions. It can be very expensive to import stuff, as mentioned above; especially if it was made in China. Also, interesting stuff simetimes vanishes & never arrives. Shipping times are unpredictable; days can turn into several months.
Better to buy 'in country'. There are Mexican online sources, once you have a tiny bit of Spanish.