Recommendations:

Mods

Primed Fast Hands

+55% Reload Speed for Rifles. Somewhat useful on bows and battery-powered weapons, since it also reduces the recharge delay and nocking time. Still, very few builds can afford the cost of installing this mostly QoL mod. Safe to skip.

Primed Fulmination

+44% blast radius for explosive secondaries. Note that because of Euclidean reasons, this mod actually doubles the AoE's affected area, and triples its volume. Hitting an entire crowd with a single shot is the biggest DPS increase you can have. More range also counteracts the damage loss from fall-off. This mod is really good for the handful of weapons that can benefit from it at all. If you prefer using your pistols for pretty little headshots, just move along. But if you're a fan of weapons like the Akarius, Epitaph and the Sporelacer kitgun, this mod is a must have.

Primed Charged Shell

+165% Electric damage for Shotguns. Electricity isn't the most popular elemental modding choice, but the primed version is still a significant damage boost. Buy this if possible.

Primed Smite Infested

+55% Damage vs. Infested for Melee. These anti-faction mods provide respectable boosts, especially since status effects double dip on them. But in normal play, they require too much micromanagement to be effective. Since there isn't any endgame activity specifically using Infested, only get this if you are planning on doing 4 hour survivals at Zabala.

Weapons

Baro's weapons typically fall into low A or B rank in tierlists, so DE at least tries to justify their asking price. And even the trashiest of weapons are worth buying if you need the Mastery Rank they provide. Or if you have good riven for them, since their disposition is usually quite high. On the other hand, Warframe has a massive arsenal, and for every weapon Baro sells, there's gonna be another that can do the same job just as well, or even better. In that sense, everything in here is "safe to skip."

Prisma Obex

A decent sparring weapon with good stats and a wacky augment centered on ground finishers. Great for Star Platinum cosplays. Get it if you like that.

Quanta Vandal

One of the weirder weapons in Warframe, the Quanta Vandal fires two electricity-based converging laser beams, while the altfire is a floating wireframe cube that can be detonated by the primary fire for massive damage. For all its quirkiness, and decent stats, it's still unremarkable performance-wise.

Cosmetics

Ki'teer Reverence Ephemera

New! An Ephemera of rippling shockwaves over and around your frame's feet. If we could equip step- and body-Ephemeras at the same time, this would be a solid fashion choice. As it is now, I can only recommend this to fans of the more understated styles.

Prisma Edo Armor Set

A set styled after samurai armor. A good ninja is a master of disguise, are they not?

Domus Syandana

Because who doesn't want to wear a tiny Liset on their backs?

Lemnas Staff Skin

A staff skin. Originally a Tennocon reward. It's up to you to decide whether it should be described as vibrant or garish.

Elixis Latron Pistol Skin

With this, you can make every single pistol look like a brass instrument. (Would that make the Prisma Angstrum a bazooka?)

Ki'Teer Atmos Oculus

Visors most futuristic, for your Operator.

Taxon Desert-Camo Skin

No, putting digital camo paint on your Sentinels won't stop them from aggroing enemies and getting shot to death 10 minutes into the mission.

Liset Prisma Skin

Mantis Prisma Skin

Landing craft skin with large sections covered with the glossy, animated Prisma looks. Allows for some very vibrant colors, but a lot of the color channels have an unremovable bluish tint. This, combined with the unusual lighting of the customisation screen, makes it hard to create the looks you actually want.

Mirage Immortal Skin

An asymmetric paintjob for Mirage. Can be used with Prime detail, but it still retains the default skin's rubberiness.

Deimos Scissus Prex

Prex cards depicting Deimos-associated entities. These were given away like candy during the Heart of Deimos update. If you haven't got them then, you can get them now for a modest price.

Prisma Companion Poster

A cool looking poster. Presumably holographic, because it's infinitely thin and floats a few centis off the wall.

Blue Ki'Teer Safari K-Drive Scrawl

A somewhat abstract image of Baro that you can put on the underside of your K-Drive. Notably less... organic that than the usual art style of scrawls.

Aged Claret of Denas

An Orokin-styled wineglass decoration. Assuming that red liquid IS wine...

Bekran Zaft's Equipment

Bucket Prime! Omni-Voice would be proud. Comes with a bamboo-handle mop which fits with the Umbra aesthetic more than it has any right to be.

Fae Path Ephemera

One the older step-Ephemeras, and rather insubstantial compared to, say, Eros Wings or Vengeful Charge. A permanent fixture of Baro's repertoire.

I might have sharp and opinionated remarks about these items, but I'm not the fashion police. Buy whatever cosmetic tickles your fancy!

Other

Orokin Tower Extraction Scene

A Captura scene of the extraction tile from the Void levels. Buy it if you want to do photoshoots in that location.

If you haven't played Sands of Inaros yet, buy the quest key and do it (and bring your best setup for scanning Kavats). If you have Inaros Prime, you can buy the Baro Void-Signal (one per visit) to access some special cosmetics.

Also, check the answers below for second opinions.