To find a specific item on broker, you have to click on the dropdown menu on "Type: Relic", then switch the Relic to what type of Avatar you're looking for.
You then type down the full item name/keywords into the search, & it should show, depending on whether or not the item you're looking for is up for sale.

I'd give you a general price range for each item, but none except the Warden of the Clover (Sakura) is currently up for sale.
But what I can say that they're all likely to be 100k+ each.

The best time to look for items is during the fest they're released in. The Full Moon Background will be coming next during Fall Fest. It shouldn't be too hard to find once fest starts. For a background that one is pretty common. In my opinion if you pay more than 150k for it you're overpaying.

Thank you both.

[Wisiro] - That's really helpful. I'm use to just putting a name in a search bar that doesn't specify. On Subeta we have an "all" search along with specific categories. So the searching system was a bit confusing for me and figuring out what category was a little confusing as well. But I think I understand more or less how it works now.

[Sakina] - So these are items that come back yearly during certain events?
That's a hefty price for sure. Though currency seems pretty easy to get if you are active on here.
I have 50k so far atm. Not sure what the best method to make currency is but I've been sending 3 of
my pets on missions.

All 4 of the big fests (spring, summer, fall, winter) have Retired Chests that you can buy from the fest shop for fest tokens. Each chest will contain a random item from a previous year. They're a decent price and if you are able to do boss runs several times a day then you'll probably make enough tokens for 1 or 2 a day.

For backgrounds that's actually a cheap price. Most backgrounds are much more rare and you'll usually find them for sale around the 500k-800k area. But the Full Moons are a blue border which means they're pretty common. Almost all the recently released backgrounds have been the much more rare orange background.
Honestly? I wouldn't be surprised if the Full Moon backgrounds are found for 50k or so during fest. But it really just depends on how common the retired chests end up being during fall fest this year.

Money CAN be a bit difficult to come by for those new to the site but it's really quite easy after you get used to things. Once you get to the Lost Grove (the current end area of the storyline) the armor drops from enemies can be sold back to the site for 2-3k each. You can make money pretty quickly that way. Missions are awesome, of course, and once you unlock all 6 slots for that you'll be able to make even more that way.