Do NOT breed a tricolor to a black. Tri, of course, is a rabbit with broken and harlequin genes. Harlies should be agouti-based. Black is a self-based color, if you introduce self genes into a tricolor breeding program, you run the risk of getting self-based harlequins, which look like torts with a harlequin overlay. When that happens to a tri, you get a lot of smut on the nose and ears, and a savvy judge will DQ it. I can think of a number of non-showable "whoopses" that could come from such a cross, so yourself a favor - don't go there.
Red is an agouti-based color, so you are safe in that respect. Since agouti is dominant to self, it is possible that both parents may carry (but not express) self genes, but the likelyhood of getting self colored offspring is much less. In addition, harlequin is dominant to red, so you will see for sure whether any bunny inherits the harlequin gene. If the doe comes from an all-tri breeding program, she may well be homozygous for harlequin, so it is possible that all of the babies will either be tri's or harlequins.
Whether you breed to a solid or a broken red is entirely up to you. I personally do not breed broken to broken, because roughly 1/4 of the offspring from that sort of breeding will inherit the broken gene from both parents, and be what we call a "Charlie." Charlies have very little color on them, so they are not showable. The gene that creates the broken pattern also is involved in the development of the digestive system, and rabbits that are brokens have "reduced gut motility" (their digestive tracts run slower). The normal brokens usually don't have problems, but those that got a double dose of the gene (Charlies) have noticibly sluggish systems, and are more prone to G.I. stasis. Whether you breed to a solid or a broken, only about half will be showable brokens (tri's). If you breed to a solid, all of the other half will be solids. When you breed broken to broken, as I said, half should be showable brokens, roughly 1/4 will be solid, and 1/4 will be Charlies. [Those numbers depend on a large number of offspring being produced, of course. In a group as small as a single litter, you could have (for example) all solids, even if both parents were brokens!