Hi Carol and thanks so much for this question.
This is a great method of introduction; slow and steady makes things easiest all round.
Yes, I would make the introductions to inividuals first, which will be easier for all to cope with. It also means a higher chance of success.
Once you (and they!) feel ready for a real meeting, give the new cat and one of the resident cats access to a neutral room that neither of them sleep in or have belongings in. It's best to not have either cat picked up in your arms so they have the freedom to do what they choose. Ensure they each have an 'escape route', as well as high pieces of furniture or cat trees to run to.
Quite commonly at this stage, once cat may choose to run away and hide. This is fine; let them take things at their pace & do not force a meeting.
The first few 'meetings' may only last a minute or two. This is fine, either cat may be finding things a little overwhelming.
In the initial few weeks, the cats should be supervised when together at all times.
Once this has been done, we can repeat with the other resident cat.
Invest in a plug-in adaptor called 'Feliway Friends' which can be plugged in the wall and will release 'Happy cat pheromones' to encourage bonding.
Consider giving all kitties a few weeks of calming supplements in their food to take the edge. These are safe, all natural products that can really help. Examples of brands include Zylkene and Nutracalm, though there are lots out there.