Currently, as of U12, there are too many weapons to individually describe, however, a quick guide in what to go for is included below. Regardless of what Warframe you choose, your standard issue weapons are:

Secondary: Lato

However, once you have 25,000 credits and you have hit rank 30 with your MK1 Braton, buy a Braton. The increased fire-rate and damage really helps untl you get better weapons. By rank 2, you now have a option to all your weapons, and you can get these via the Market.

By Rank 2, these are what are recommended, however, you will have to use all weapons at some stage as you need the points to go towards your mastery rank. The 'Rhino' warframe is also unlocked.

Primary: Paris (You can get this at Rank 0, but you really need a stealth or tanky frame to use this), Boltor, Karak

Melee: Scindo, Dual Heat Swords, Dual Zoren, Orthos (HIGHLY RECOMMENDED FOR RANK 3-4 MASTERY TEST)

So, when you hit Mastery Rank 4, you would have collected a good amount of resources. You may need to go hunting for a spare morphic or neurode, but you should be fine overall. Rank 4 is where all the market melee weapons become available to you, and there arises the need of Galium. Try recruiting a squad for a Survival or Defense and use Rhino. If you are desperate, ask your team mates to mark Gallium out ('G' is the default waypoint key)

My recommended loadout by Rank 4 is:

Primary: Karak/Boltor, Miter(only if you have completed the Assassination mission on Illiad, Phobos)

Secondary: Hikou (Kunai is your other alternative, but be prepared for long flight speed and low fire rate), Twin Vipers/Twin Gremlins (again, you need to have done the Assassination mission on Illiad, Phobos)

Melee: Nikana, Galatine, Fang, Ether Sword, Dual Ethers, Bo (This is a very under-used weapon, but very good if modded right)

Rank 6 is the rank in which you can buy everything in the Market. This is a highly anticipated rank due to the unlocked weapons.

Primary: Penta, Soma (This thing has a high crit rate, so crit builds would benefit it greatly)

Secondary: Hikou (You don't unlock secondaries past Rank 2, excluding Dojo weapons)

Melee: Dakra Prime (Yes, the first prime. Do NOT try farming prime weapons in the void until you are Rank 6 as you need to farm high level survival for these keys, and the enemies in the Void itself require very advanced modding. In most cases, you will simply hinder your team mates by going down over and over again.)

From Rank 6, you will have to start using prime weapons at higher levels (this excludes high dps weapons such as the Ogirs, Ignis, and Soma). From all your survival and defense missions, you would have plenty of void keys (accessible in your top right navigation bar). Prime weapons are improved versions of their market counterparts, and often possess 1 or more polarity slots (polarities halve mod costs).

Recommended Prime weapons:

Primary: Paris Prime, Latron Prime, Boltor Prime (The boltor prime is very difficult to get, especially the blueprint)

Secondary: Lex Prime, Sicarus Prime (Honestly, I would stick to market/clan sidearms, currently the Prime sidearms are nothing special)

Melee: Orthos Prime, Reaper Prime, Dakra Prime, Glaive Prime (Orthos Prime does have the highest DPS for melee weapons, and should be your first choice, as its parts drop from Tier 2 Void missions)

Dojo weapons are weapons you and your clan (hopefully you do have a clan) research in labs you must build, and they take varying times. Be generous, as you will also benefit. However, some weapons and items will exhaust your resource, so be selective. Confer with your clan mates and decide how to prioritize your resources and time.

You can learn about all the weapons on the Warframe Wiki, here.