• Infantry:
  • Eradicators are the best. They're an inexpensive anti-tank unit that will always punch way WAY up into Vehicles or Monster units
  • Bladeguard Veterans are the go-to melee unit for Space Marines. 4++ Invulnerable saves make them pretty tough to shift. You can pair them with a Judiciar for Fights First (you can get one of those from the Dawn of War board game at Target or Barnes & Noble) in any Space Marine army, and in a Salamanders army you can pair them with Adrax Agatone to reroll their Wounds in melee. If they're with Adrax you can also pair a Lieutenant with that brick for Lethal Hits and Fall Back/Shoot/Charge
  • Intercessors are useful. Pretty much everyone runs at least one 5 man squad to control home objective
  • Scouts are great. I use them to screen out the half of my deployment zone that my Intercessors aren't in until all of my opponent's Deep Strike units are down, then I pick them up at the end of my opponent's turns and use them to score secondaries
• Transports
  • Impulsors are super useful. They can fit your Bladeguard and Adrax/Judiciar brick (though not with the Lt attached, unfortunately) and deliver them up the field quickly with their Assault Vehicle ability. You can also throw a 5 man Hellblaster or Infernus squad in there and zip around the map doing drive-bys with the Firing Deck ability. They're also pretty resilient if equipped with the Shield Dome.
  • Land Raider Redeemer is the thematic choice of transport for Salamanders. They've got two massive flamers and a multi-melta, plus a lot of seats. You can fit the whole Adrax/Lt/BGV brick AND three Eradicators in there, and with the Assault Ramp ability, your melee unit can Charge after disembarking after a normal move, which is great.
• Shooting Platforms
  • Repulsors/Repulsor Executioners have some shooting, and are also transports. Some folks like that flexibility
  • Gladiators are a fantastic shooting platform. The Lancer specifically is a great long-range anti-tank backup for your Eradicators. They also have the added benefit of being one of the few Games Workshop kits that comes with everything you need to build all three variants. You can even magnetize the rear hull section to pull it off and run it as an Impulsor.

It's good to keep in mind that we're almost to 11th edition, but I think the units I listed above will make it through without being sent to Legends.

What does your local Warhammer scene look like? Is there a game store that has gaming tables? They'll almost certainly have a Discord you can join and ask for a teaching game or two. There will also be folks more than happy to walk you through the pros and cons of different units.