Hi mutty62,
That depends on the type of mattress you end up purchasing and on the condition of your box spring. Post #2 here has more about deciding on whether it would be a good idea to keep your box spring or replace it.
Yes … if you are planning to use a 4" memory foam topper on your mattress then it would be a good idea to purchase a mattress that was significantly firmer than what you would normally choose if you were using a mattress by itself with no topper. In a “perfect” world it would be a good idea to test mattresses with your topper on top of them to see which combination was a good match for you in terms of PPP (Posture and alignment, Pressure relief, and Personal preferences) because a topper can feel and perform differently on top of different mattresses but this probably isn’t practical so the best you could do to offset the risk of buying a mattress that was too soft for your topper (which would be risky in terms of support/alignment) would be to buy something that was “very firm” and had little in the way of comfort layers because in effect you are adding your own comfort layer to the mattress.
I don’t recommend “brand shopping” at all because outside of how well a mattress “matches” your specific needs and preferences in terms of PPP, a mattress is only as good as its construction and the quality of the materials inside it regardless of the name of the manufacturer (see post #5 here). There are also hundreds of mattress manufacturers across the country and many of the better ones (such as OMF) that are more transparent about the materials they use inside their mattresses are only available locally or regionally so it would depend on where you live.
Having said that … OMF is transparent about the materials they use in their mattresses and in most areas of the country would be good quality/value compared to many of the other options that are available to you.
Just in case you haven’t read it yet I would also make sure you’ve read the mattress shopping tutorial here so you have the basic information, steps, and guidelines you will need to make the best possible choice. If you let me know your city or zip code I’d also be happy to let you know about any of the better options or possibilities I’m aware of in your area.
Phoenix