Hi Meg,
You can save seeds. It all depends on what you are actually growing. Cucumbers, Cucumis sativus, will only cross with other cucumbers. True gourds, Lagenaria siceraria, will only cross with other true gourds, but some gourds are actually squash, Cucurbita pepo. But those squash gourds will only cross with certain types of squash like zucchini and acorn squash which are also Cucurbita pepo. Squash, Cucurbita will not cross with Cucumbers, Cucumis. Are you confused yet? lol.
It really would be best to see a list of all the things you plan on growing and figure it from there.
Scarlet Runners and Kentucky Wonders will not cross. Though both called beans, they are not the same botanically. Scarlet Runners are Phaseolus coccineus. Kentucky Wonders are Phaseolus vulgaris. Their second name part, the species part are different and that means(in general, there are a few odd exceptions with plant crossing)that they are not able to cross with each other.
So for all you grow, if the first and second in Latin match, you can get crossing.
Brassicas cross freely, but some are biennials so saving seed is difficult to begin with since overwintering is need to procure seeds. You of course can grow broccoli or rappi and save seeds from them since they are first year bloomers.
Oh, tomatoes in general can be planted pretty close and no crossing can occur.
Hope this helps some,
Remy