For softcore players, SuffixCold Resistance should be prioritized over SuffixHealth once you swap over to ward. You get no ward benefit out of adding health, it's simply a cushion for one-hits and is a big advantage over low-life set ups. Transitioning out of life into ward has been a continuous process for me as I slowly lower my health pool in exchange for boosting PrefixIncreased Healing Effectiveness and SuffixCold Resistance.
Weapon
Apathy's Maw offers an extremely robust set of offense and defense stats but is by no means required.A Great Cutlass,Odachi,Orbit Cleaver,or Obsidian Axe would serve very well for a long time with the right stats and can definitely outshine an Apathy's Maw without LP. A "good" weapon for Rive can take a lot of different forms especially before you swap to using ward. Prior to being able to use Citadel Boots and Leonine Greathelm you will want SuffixReduced Bonus Damage Taken from Critical Strikes but also be able to utilize any combination of SuffixChance to Shred Armour on Hit, SuffixChance to Ignite on Hit, PrefixMelee Physical Damage, PrefixMelee Attack Speed and PrefixPhysical Damage. Unfortunately the stuff that makes PrefixVoid Damage worthwhile doesn't really start synergizing until pretty late in the game.
Armor
Titan Heart and Champion Regalia offer solid bases for LP or crafting for endgame. While Titan Heart is fantastic at 0 LP it will eventually be outclassed by a good exalted. Playing Whack-A-Mole trying to get a good stat onto 1lp might not even be worth it. I usually end up with a Solarum Plate along the lines of Solarum Plate due to the difficulty of obtaining the other 2 but I am always looking.
Rings
A Sunwreath with LP also works well but doesn't provide much benefit without the slam. A Siphon of Anguish is a little bit redundant because of 100% Doom chance from Apathy's Maw but CoF players coming from leveling will likely have one slammed pretty good before dropping the Apathy's Maw
Boots
Citadel Boots are the endgame goal, so use whatever's available before then. If you are eager to start your ward career 0lp Last Steps of the Living offer a solid beginning option with SuffixCold Resistance or PrefixExperimental Frenzy Effect doing a lot of work for 1lp.
Gloves
Frostbite Shackles with T1 or T2 PrefixExperimental Ward per Missing Health are the perfect 1 step solution to retention and conversion for Healing Hands. Before that a Swaddling of the Erased provides a lot of generic benefits and any gloves with PrefixMelee Attack Speed can round out both defense and offense.
Helmet
A Leonine Greathelm pairs well with Citadel Boots and provides tons of SuffixArmor and Reduced Bonus Damage from Crits from its implicit. It even rolls high enough to cap it with a extra t2 affix and free your boot slot. PrefixLevel of Healing Hands takes priority but is very expensive, t5 is alright. PrefixLevel of Anomaly is also great because it will boost your buff or debuff capabilities significantly along with PrefixVoid Damage.
Belt
Shattered Chains with LP is a lofty goal to set but is very rare so Spidersilk Sash and Praetorian Belt both work well in the interim with a helping of SuffixCold Resistance and SuffixHealth
Relic
A Code of an Erased Sentinel works so well it's one of the more expensive items on the list. Argent Crest works well for ward purposes and a Soulfire helps early to generate Flame Drinker's Blade 1/1 stacks through Healing Hands and Divine Bolt hits.