Take what I say with a grain of salt because I am not a veteran zombies player, however I found some things that might help

Never ever back yourself into or run into any corners, especially later rounds because there are a few (such as one of the signs by the concrete blockers near Crusader's Ale) that are tough to get out of

Building the zombie shield first will save you so much stress, so make sure you prioritize that

Perk Buying Guide:
Quick Revive, Stamin-up, Jugger-Nog, (the two perks on the open roof area), Mule Kick, Vigor Rush, (the perk by the PAP), Electric Cherry, Deadshot, Double Tap, Banana Colada, (the perk outside the church area), (the ice perk inside the grocery store), Speed Cola, Crusader's Ale, Elemental Pop, Widow's Wine

Make sure you grab Elemental Pop before you fight the boss as this will make the fight easier
(It's also necessary for later rounds)

If you get the Thunder Gun, Wunderwaffle, or Maelstrom of Eris, never give them up. These will be vital for later rounds

(Assuming) you have the TG and WW, make sure you use the TG to kill one large crowd while circling, and the WW to target long strates of zombies. This will kill them more effectively and efficiently

Widow's Wine should (probably) be the last perk you get, as this will be really helpful during the ritual

Don't bother buying the first two wall weapons you see (assuming you get a max ammo or another drop to get you more points). You can reasonably stay in the first two areas til Round 6 or so, enough to buy the MAC-10 outside of Speed Cola

The Fireworks gun perk is the best to kill large groups in later rounds, though Turned can also be helpful

Only go for the box in the upstairs levels if it reasonably safe to do so as escape routes are tight and don't leave much room