Airport transfer

Train or bus to the central station. Then metro or tram or bus or walk, depending or where the hotel is actually located.

I guess it depends on how you define "best".
With four people plus luggage I would think that a taxi would be a cost-effective option for your family, and the convenience of the door to door service would minimize any hassle involved and thus might be worth the extra cost involved.

If cost-effective means, an effective way to increase the cost of the trip, then yes, taxis are very cost-effective. 😀

You might want to check with your concierge at the hotel to see what they suggest.
A taxi will no doubt cost more than the train, but for a family of 4 it might indeed be a more convenient option, particularly with a favorable exchange rate between the SEK and the USD.

The Arlanda Express train costs 420 SEK for 2 adults. Children under 18 travel free with accompanying adults. So that will get you to Central Station, but then you will have to go by one of the frequent buses to Slussen bus stop by the Hilton Hotel.

Internet is telling me a fixed rate taxi with up to 4 passengers is in the 500 SEK neighborhood. In this case, I'd go with the taxi.

So that will get you to Central Station, but then you will have to go
by one of the frequent buses to Slussen bus stop by the Hilton Hotel.

Or two stops on the metro.

Internet is telling me a fixed rate taxi with up to 4 passengers is in
the 500 SEK neighborhood.

In that case you need to update your internet, 750-800 kr is a more realistic figure for a taxi.

Slussen T-bana station is a few blocks from the Hilton. Slussen bus stop is right there.

Yes, should looked at the official Arlanda website. 750 SEK fixed price to central Stockholm.

Slussen T-bana station is a few blocks from the Hilton. Slussen bus
stop is right there.

If you are thinking about the bus stops just north of the city museum, they don't exist anymore. The metro station is closer than the bus stop. The metro is also a lot more frequent than the buses.

There is of course also the option of taking a taxi from the central station to the hotel.

We took a Flygbussarna bus from the airport to Stockholm. You buy tix online ahead of time and scan the code with your phone upon entering bus (NO paper tix allowed). Bus driver was helpful. We had to scan code twice as there were 2 of us-- but did not need to change the phone's screen. We had to find the stop outside the terminal, but it was fairly straightforward once we knew to search for Flygbussarna logo. Bus ride was great. Guessing your hotel may be able to tell you which bus number to take.