I'm not sure, but I think Beefmaster was introduced originally in 1971 as Beefeater, a Peto bred product, but had a name change due to obvious name conflict with a famous gin spirit.
I've seen Beefmaster alternately described in seed catalogs as determinate and indeterminate, but in any case it appears to be an F1 hybrid. Can you say whether what you grew was determinate or indeterminate, because that may be the first consideration you might give in selecting a line toward stabilization. However, I tend to believe Beefmaster is indeterminate.
Beefmaster also carries resistances for V, F race 1, and N according to most catalogs. I've also seen catalogs say it's resistance to gray leaf spot and crown wilt, so if those are a problem for you, you may want to observe the tolerance level of your selections for those diseases. If you are growing in sandy soils where nematodes are common, you may want to field test residual for N-resistance when selecting your line.
Sometimes breeders will use a breeding line with a pronounced nipple to prevent indented or deformed blossom scars in the F1 hybrid. This is seen in Celebrity, for example, and sometimes when you grow out the F2 seeds, you will get a reoccurance of this feature. Don't be alarmed or don't automatically discard such a plant, because it may develop into a nice appearance without catfacing or blossom end deformities as your dehybridization progresses.
I wouldn't necessarily concentrate on replicating the F1 hybrid as exactly as possible unless that is exactly what you want. Rather, I would select for flavor, production and vine health. It might also be beneficial to look for a growth habit that stays within the limits of whatever support system you use, like cages or stakes, and is adaptable to whatever other growing conditions you have, like containers, raised beds or whatever type of garden you have.
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