You can certainly go WiFi with the modem and router you just bought and get a decent picture without lag. I’ve done it while testing out the Fire TV in a number of scenarios using Vue. But I prefer to use Ethernet because it greatly lessens the chance of running into lag. My router is close to my Fire TV box so connecting them with an inexpensive Ethernet cable makes sense.
DIRECTV: This satellite provider was purchased by AT&T in 2015. Their package prices tend to be higher than Dish Network, but you do have a choice of six different packages as opposed to Dish's four. Football fans will find this choice a no-brainer as DIRECTV is the only one of the two companies which offer NFL Sunday Ticket. Check out the full DIRECTV channel lineup here.
The question of "when does it make sense?" can easily be rephrased as "how much money can I save?" and one of the biggest factors will be the price difference between combined internet and TV service or just internet. These are also the options that vary the most widely based on where you live, and the availability of promotions or contracts that can keep prices down for a short time.