There is no train service to this town.
There are four direct long distance bus services daily operated by rede-expressos.pt
Departures are from Lisbon Sete-Rios Long distance Bus Station. Timetable as follows -
One way tickets cost € 16.00
The easiest way to get to Sete-Rios from the Airport is buy Yellow Bus Tours Bus Line Nº2 that operates from the Airport every 40 minutes. Cost is € 3.15
Website here: http://bit.ly/12uNdIe
Taxi is another option. However, prices can vary owing to time of day, size of vehicle and no. of bags.
I would check your best option on arrival at the Lisbon Tourism Desk which is facing you as one exits the baggage hall into the arrivals concourse. .
As regards car hire, this may be a problem. VNM is isolated and does not as far as I know have any car hire companies with offices in the town. A quick search of the web suggests that Hertz.com and Europcar.com have agencies in the nearby Port of Sines (30kms distant). They may be able to come and collect a vehicle from VNM.
As regards ATM's Portugal, has a an excellent independent national network which accepts most international cards within daily limits. One would have to check with one's bank, card company or shop around for the best deal to find the most cost-efficient option.