The first rig can be an intimidating decision, and there are a lot of different factors that can go into it, including what you want to do and how much money you have to spend. I'll be discussing various options from absolutely free to about $1200 dollars, and what I talk about will definitely be impacted by my own experience and preferences.
I will also be focusing more on VHF/UHF than HF, although I will talk a bit about a DC to Daylight rig.
The beautiful thing about Echolink is that it is free, and most people these days will have access to either a cellphone or a computer. I have installed it on both iOS and Android, as well as on Windows and OSX (OSX via Wine). You'll be able to talk to other hams both via Echolink conference nodes and by connecting to repeaters.
Here we're talking about a purchase in the $150 range that will get the new ham on the air with DMR, D-Star, and System Fusion. This may be a very good option to pair with a sturdy and affordable Yeasu HT. The DVMega DVStick30 is a very versatile and well-supported option.
Here is where personal preference and intended use really make the difference. If you're planning on operating satellite, for instance, you'll choose a different HT than if you're planning on operating around town.
ID-51a
TH-D72A -- this is the HT I would recommend for satellite operation. Full duplex which is a must when operating satellites. Pair this rig with an Arrow antenna and you're off and running.
TH-D74A -- I don't own one of these yet, but definitely plan on getting one.
FT-65R Dualband (2m/70cm) HT, under $100 everywhere I've looked, and as such is a great bargain. If you pair this with the above DV Stick, you can fully get on the air for under $250, getting access to FM via this radio, and digital voice via the DV Stick
All three of these HTs will work very nicely with the N9TAX J-pole antenna. I have mine up against my window and I hit repeaters miles away consistently.
Honestly, I'm not sure I can make a recommendation here. I would probably buy an Icom 5100 if I was in the market for a new mobile VHF/UHF rig.
For a first base HF rig I would recommend the Icom 7100 -- it is a "DC to Daylight" rig with HF/6m, 2m, and 70cm. This lets the new Technician get on the air, and also gives them the ability to experiment with HF. I would recommend the LDG IT-100 as a very capable tuner for Icom gear, and it also pairs very nicely with the N9TAX antenna recommended earlier.