Here is my build: https://overframe.gg/build/386728/frost-prime/archon-thermal-sunder/
Energy cost isn't a problem with high efficiency and zenurik. Don't really need range since i usually move from pack to pack. I even put a lot of utility in my build with Mecha set and icy avalanche. I once out damage people in SP circuit with this build.
Kuva Ogris. I also really like Shedu with one toxin mod to produce gas and corrosive. If you use a frame with nourish for viral, the damage is amazing. Main weapon on my revenant.
I really love what happened recently to the game with helminth and armor rework and archon mods. Frost is in a decent spot IMO. Some additional tweaks would be welcomed for his passive, 1 and 2, but I replaced his 2 with Thermal Sunder and use his 1 as utility to shatter his globe. The full armor strip on his 4 is amazing and thermal Sunder makes him a decent caster frame, where you can actually kill enemies with abilities.
My man Frost!! love him with Thermal Sunder and Archon Vitality.
not sure if you're on PC or console, but it's quite easy to get plats by trading with other players. check out warframe.market, there are some stuff quite easy to farm, but mostly prime parts.
the base mods are usually serration (rank 6 is good enough when you start), multishot and ele damage. viral (tox + cold) or corrosive (tox + elec)
attack speed and crit damage is usually the way to go with melee. But like @Retrikaethan, heavy efficiency can be quite good as well. I would go with attack speed, crit damage and ele or heavy efficiency.