Good morning Karyn,
I grow the actinidia arguta variety and it hardly seems invasive. There is no different coloration between the male and female, and they slowly wind around their respective trellises/fence. The leaf is large and fuzzy/hairy. They stay where I put them. You are describing the fruit of mine too; it is the commercial variety grown in Australia and Europe for retail, so I'm thinking that's what you have too.
However, the vine does get quite large, over 30 feet. But it will take it years and years to do this, I've heard 5 or 6.
Mine are young, between 1 year and 2 years old. The 2 year old is about 6 feet.
As far as looks, the leaves are heart shaped, big and fuzzy. The actual stems are pretty (imo) and bright green with lovely red hairs all over them.
Perhaps someone who has older vines can tell you if it invades from ground suckering. Mine don't look at all like they do that, and trimming the tops would keep it shapely.

I forgot to mention, I have heard they actually enjoy being root bound, so you could always leave in large sunken pot underground if you were worried about roots spreading out too far.

Here is a link that might be useful: Details on Arguta

Thanks. Thinking about it these might have been imported from New Zealand. My female vines sound like what you describe. I should clarify that mine didn't send runners but they eventually just got so big and very heavy. My vines were about 10-12 years old and I started trying to remove them about 3 years ago. I never thought about sinking a pot. That might work. I enjoy the fruit but can't deal with the monster vines.

passion4passies looking at your username I assume you grow passifloras. What varieties do you grow? I probably grow as many varieties of passies as brugs.

Speaking of passies, do either one of you grow Passiflora Riperia? I've had that plant for a year and it hardly grows or does anything lol. No clue what it wants. I've tried moving it around in different light situations etc and still that same thing...
It is supposed to look like the one in the link below

Here is a link that might be useful: P. Riparia

I have no idea about that one but I really like it a lot. You might want to shoot Eric or Crystal (husband & wife) an email. Eric posts often on the passiflora forum and has more varieties then Carter has little pills.

Maybe I will. I cannot figure out if it is just a slow grower or if I don't have the right type of enviornment for it here. I hope it isn't one of those that likes cooler weather. I have had it 2 years.

I sent Crystal an email about your passie. If she knows anything I'll let you know. All I found online were pics, no info. I don't even know what subgenus it's in, maybe passiflora?

Yep that's it exactly, all pics and no info. It might not even like it here lol.

On kiwis: I only have the fuzzy type. I bought a female and male plant combo in a pot at Lowes for 3.oo last fall. I thought they had died off this winter but turns out they were just dormant. I know nothing about them :P
I have a book called, Florida's Best Fruiting Plants. It has good info on the more unusual tropical fruits as well as the common ones. It says that the kiwi isn't especially well suited for FL but I will try it anyways. I was thinking of trying to root some more of the female vine in order to have more females per male. Has anyone rooted kiwis?