Kiwiberries are quite resistant to disease, but they are susceptible to phytophthora root rot in excessively moist soils.  Conversely, soils that dry rather quickly can dramatically slow growth for at least a few years. 

kiwis require low to moderate effort to manage.  However, fruiting shoots are quite vulnerable to frost damage throughout most of the country, but damage strictly to young leaves can be insignificant.  Some varieties developed in the south may awaken much later than most, but none of them are from species referred to as kiwiberries. 

Hardy kiwis are borderline invasive.  Arctic kiwis are easier to control.

Hardy Kiwi
Actinidia Arguta

Anna

Originated in Russia
Alias
• Ananasnaya, Annasnaya
Zone
• 4b
Ripens
🥝
• late
Color
• green skin with a purple-red blush
Fruit
• small-size, up to 14g/berry
Yield
• highly productive

Chang Bai

Seedling of Qui.  Selected in China near the border of North Korea.
Zone
• 4b
Color
• green skin
Fruit
• medium-size
• flat pumpkin shape

Cherry Bomb

Zone
• 4
Color
• red skin

Cherry Bomb might be a cross between A. arguta and A. kolomitka.  If so, it could be hardier than zone 4b.

Chico

Zone
• 4b
Ripens
🥝
• mid-late
• ~1 week earlier than Anna

Chico kiwis easily separate from the stem.

Cordifolia

Zone
• 4b
• low chill
Color
• dark green skin
Fruit
• relatively sweet?

Cordifolia may also be referred to as 'Meyer's Cordifolia' to avoid confusion with another variety that is now being referred to as 'Early Cordifolia', but I don't know the full story.

Dumbarton Oaks

Selected in Georgetown, Washington D.C.
Zone
• 4b
Ripens
🥝
• early-mid
• ~3 to 4 weeks before Anna
Color
• light green skin
Fruit
• pumpkin-like shape

Fifty Five

Zone
• 4b
Ripens
🥝
• early
• roughly 6 weeks before Anna

Flowercloud Male

A. arguta x A. kolomikta
Zone
• 4b?

Flowercloud may begin to flower as soon as the year after planting, but it blooms earlier in the season than arguta males due to its hybrid parentage.

Fortyniner

Developed in Chico, California.
Zone
• 4b
Ripens
🥝
• mid-late
• somewhere between Dumbarton Oaks and Anna

Fortyniner might be the same cultivar as 74-49.

Geneva

Selected in Geneva, New York.
Zone
• 4b
Ripens
🥝
• mid-late?
• somewhere between Dumbarton Oaks and Anna

Hardy Red

Zone
• 4b
Color
• red skin

Hardy Red has supposedly done well in taste tests, according to nurseries.  I have not seen any results or heard about this cultivar elsewhere, though.

Issai

Originated in Japan
Zone
• 4b
• 300 chill hours
Flowers
• partially self-fertile
Color
• green skin
Fruit
• small-size

Issai grows less vigorously than most arguta varieties.

Jumbo

Originated in Italy
Zone
• 4b
Color
• green-yellow skin
Fruit
• medium-size, up to 28g/berry

Jumbo produces large berries for a hardy kiwi, roughly twice the size of Anna.  It may be the same variety as MSU (Michigan State).

Ken's Red

A. arguta x A. melanandra.  Originated in New Zealand.
Zone
• 4b? (5)
• low chill
Ripens
🥝
• late?
• somewhat biennial?
Color
• red skin
Yield
• highly productive

Meader Male

Zone
• 4b (4a)    ◦ one report claims it survived down to -28F (-33.3C)

Natasha

Originated in Vladivostok, Russia.
Zone
• 3b

Prolific

Zone
• 4b
Flowers
• partially self-fertile
Color
• dark green skin

Red Princess

Cordifolia (A. arguta) x A. melanandra.  Originated in New Zealand.
Zone
• 4b? (5)
Color
• red skin

Rossana

Selected in Italy
Zone
• 3b

Tatyana

Zone
• 3b
Color
• light green skin

Arctic Kiwi
Actinidia Kolomikta

Arctic Beauty Male

Zone
• 3a

The leaves of Arctic Beauty develop white and pink colors, especially when they are exposed to the sun.  It may last for a month or so, but then it fades out to a light tan color.

Emerald

Zone
• 3a
Color
• light green skin

Frost

Zone
• 3a
Ripens
🥝
• early? (early-mid)

Frost ripens earlier than most Kolomikta varieties.

Hero

Selected from the wild near Vladivostock, Russia (Far East).
Alias
• Dostoynaya
Zone
• 3a
Color
• light green skin

'Hero' has an unconfirmed report about being partially self-fertile.

Pasha Male

Zone
• 3a

The leaves of Pasha develop white and pink colors.  If 'Pasha Male' is similar to 'Arctic Beauty Male', the colors are amplified by exposure to the sun.

Red Beauty

Zone
• 3a

September Sun

Originated in Russia
Alias
• Sentyabraskaya
Zone
• 3a
Ripens
🥝
• mid?

September Sun is the only female I know of that produces ornamental leaves similar to that of the arctic kiwi males.

Viktor

Selected from the wild north of Vladivostok, Russia.
Zone
• 3a

Viktor produces larger berries than most kolomikta varieties.

Golden Kiwi
Actinidia Chinensis

AU Golden Dragon

Zone
• 8a (7)
• 800 chill hours
Ripens
🥝
• late?
• matures roughly 7 weeks earlier than AU Fitzgerald
• mid-late August in central Alabama
Color
• yellow-green flesh
Fruit
• large-size, 89 g/fruit

Golden Dragon can hang on the vine for roughly a month after maturing, but the fruit will become very soft.  This may be typical for many chinensis and deliciosa varieties, and they may be able to hang much longer than that, as long as it doesn't get too cold.

AU Golden Sunshine

Selected in Alabama from material that originated in Chongyang County of China (Hubei Province).
Zone
• 8a (7)
• 700 chill hours
Buds
• break in early April in central Alabama
Blooms
💮
• late    ◦ mid-late April in central Alabama
Ripens
🥝
• very late?
• matures mid September in central Alabama
• ~4 weeks before AU Fitzgerald
Color
• yellow flesh
Fruit
• large-size, 90 g/fruit

AU Golden Tiger Male

AU Golden Dragon x unknown male (pollination occured in China).  Selected in Auburn, Alabama.
Zone
• 8a (7)
Blooms
💮
• late    ◦ along with AU Golden Sunshine

Fuzzy Kiwi
Actinidia Deliciosa

AU Authur Male

Zone
• 8a (7)
• less than 800 chill hours

AU Fitzgerald

may be a seedling of Hayward.  Developed in Summerdale, Alabama.
Zone
• 8a (7)
• 550-800 chill hours
Ripens
🥝
• extremely late
• matures mid-October in central Alabama
Fruit
• medium-large size, 70 g/fruit

Hayward

chance seedling.  Discovered in Auckland, New Zealand (1920's).
Zone
• 7    ◦ down to -2F (-18.9C)
• 600-800 chill hours
Ripens
🥝
• extremely late
Storage
• up to 6 months

Hayward is the most commercially cultivated variety.