In theory, you should not need a visa. As stated by Timatic, the database used by airlines:
Visa exemptions: holders of onward tickets for a max. transit time of 24 hours.
In my experience, however, in practice many check-in clerks and gate staff (incorrectly) interpret this as "Holders of onward tickets in the same booking for a max. transit time of 24 hours", and are thus likely to deny you boarding without a visa. One reason being that, if you miss your connection due to a delay, you're not covered by the airline and would be stranded at the Moscow airport, in which case your inbound carrier could be forced to send you back, a situation they want to avoid at all costs.
Furthermore, if you have checked-in luggage, it may very well not be checked through, in which case you will need a transit visa to pick it up and re-check it, which requires clearing immigration (both in- and outbound)
Contact Menzies Aviation at Arlanda at 08-797 80 84 (they're the ones checking you in, and, I think, checking you at the gate) to find out the arrangements regarding checked-in luggage (if you have any) and how they enforce the onward connection rule.
If you do end up having to apply for a visa, then no, you do not want "a normal visit visa", but a double-entry transit visa