How do you define "best"? The "best" way might be to charter a helicopter and fly.
The cheapest way is by bus to the border, cross over then taxi/colectivo/bus to San Ignacio.
The most comfortable way would be to hire a transfer service (or private shuttle). The one you mentioned is fairly well known in Belize -- I haven't heard anything negative about them. There are several transfer services that could take you, but you have to make your own arrangements with them. Contact each one for quotes. William's Belize Shuttle is a good one. You can find a list of Belizean transfer services on the BelizeBus website (google it).
Another way is to get a taxi from Flores to the border, walk through Immigration/Customs and then get a Belizean taxi to SI. The Guatemalan taxi to the border should cost in the order of US$50 to $60. The Belizean taxi to SI shouldn't be more than BZ$50 (or US$25).
Regarding San Juan, I've read several negative comments about their service within Guatemala, but there is a San Juan Travel Service that runs a daily express bus from Flores to Chetumal -- I haven't read anything negative about that service, so you could get that bus. It's not supposed to make a stop at SI (check with the driver -- this is Belize!), so you would have to get off at the border (after crossing to Belize) and continue by Belizean taxi/colectivo/bus.
Linea Dorada and Fuente del Norte also run daily express buses to Belize City. You could get one of those buses as far as the border -- they are also not supposed to make a stop at SI. The BelizeBus website has details of all those buses.