it appears that either the super shuttle (a.k.a. the blue van) or the airlink shuttle van offer the best combination of value ($19 one-way to manhattan) and efficiency (a relatively quick, door-to-door ride into nyc with no need to transfer):
To and From the Airport.com - Newark New Jersey
Runs shuttle vans to hotels and homes in the New York area.
Fares per person: To Manhattan hotels $19, To Manhattan residences $21 for the first person & $12 for each extra person, To Brooklyn, Queens, Bronx and Staten Island $25-60 1st person, $15-30 for each additional person. Contact: Tel (212) 258 3826 (212 BLUE VAN) or reserve on line.
Routes: Runs a direct door-to-door service to homes and hotels in Manhattan (anywhere from Battery Park to 125th St).
Cost: To Manhattan $19 one-way, from Manhatan $19, $33 round trip. Contact: Tel 1 877 599 8200. There are free courtesy phones in each terminal at the Ground Transportation info desks. Tel 24 hrs in advance for reservations going to the airport.
if you want to save money, the cheapest option would be to take the train or bus, but both have their downsides.
to get to manhattan from EWR via train, you'd have to take the airtrain (an airport monorail system) from your terminal to the newark airport commuter rail station. from there, take the nyc-bound nj transit train to the final stop (ny penn station), and then switch to the subway or a cab to get to your final destination.
obviously the benefit is the lower cost, but the downsides are the multiple transfers and the potentially lengthy wait for connecting trains, especially when switching from the monorail to the nj transit train. IMO, the savings are not worth it.
to get to manhattan from EWR via bus, you'd take the newark liberty airport express bus
Runs buses from Newark airport to Penn Station, Port Authority Bus Terminal & Grand Central Station in Manhattan. Buses run to Midtown every 15-30 mins & to Lower Manhattan (Chinatown & Wall St) every 30-40 mins. Cost: $12 one way or $20 round trip. Children under 12 free, seniors half price. Buses depart from the level below arrivals (ground transportation level of terminals A, B & C) stop 2 or 3. Travel Time: Takes 30-40 mins. Buses run 24 hrs, but frequencies are much reduced late at night. There is a desk in arrivals where tickets can be bought. Previously known as the Olympia Express. Contact: Tel 1 877 894 9155.
if i had to decide between the train and bus, i'd choose the latter. but again, the shuttle van would be my first choice.
and you're right about the taxis to nyc not offering flat rate fees:
To the city of Newark $15-18, to any other part of the airport $13-15, to Downtown & Midtown Manhattan $50-70, to East Side Manhattan add $5, to JFK airport $94, to La Guardia Airport $75 + tolls.
you should click on the link at the top of this post to review all of your transportation options. any info posted here is included in that link.