Here are the first two I check out when I want a new piece of art. I have successfully purchased pieces from both. Happy sleuthing!

https://www.sulisfineart.com/ or http://www.ebaystores.com/sulisfineart

https://www.ebay.com/str/samuelcollection

I've used Saatchi Art. They've got pretty good filters, including size, orientation, color, price, style medium, etc)

https://www.saatchiart.com/

I have a lot of art by non-professional artists, but here's one I like who has a website:

http://lindayoshizawa.com/

Following Linda's links led me to this virtual exhibition of works by California Printmakers. Pretty cool website, though it took me a while to figure out how to pull up the artist and price information. It's there though, if you click the artwork.

https://publish.exhibbit.com/gallery/71365457/long-gallery-30987/

Etsy

Artful Home

Local galleries (for me) that may at least provide inspiration if you browse their artists:

Greenhut (ME)

Powers (MA)

Left Bank (Cape Cod)

Etsy

Invaluable.com

IG pages that sell items.

Antique stores.

We bought several items from Saatchi and also from individual artists that we've discovered over the years.

I believe Daily Paintworks is the site that I have perused with interest in the past. Never bought anything here, but it's fun to look:

https://www.dailypaintworks.com/

Mostly antique stores for us, but I have found a few things on Etsy and Ebay. Obviously I prefer vintage pieces, and that may or may not be your thing.

I think the best art is personal to the people whose space it is. Think about what you and your family like to do and where you all like to spend your time. Family photos (even snapshots) can also be very eye-catching!

Some examples:

• Where have you traveled? Here's a terrific print from Miami Beach:
• Where do you live? Here's a stunning Wyoming landscape.
• Love your pet? You can get pet portraits in a variety of styles.
• Have a great family photo? You can get it blown up as a canvas.
• Do you have a preschooler? They can create really stunning images that you can have turned into framed or canvas art.

Great advice already! I’m enjoying checking out everyone’s links.

My usual MO (for online) is to start with a subject first, otherwise I get overwhelmed.

For example, we saw a few vintage quail prints locally, but they just weren’t “it”. Came home, searched ‘vintage quail prints‘ online ... and found a great one in folk art style (which I hadn’t thought of before). Plus, discovered a new-to-me-artist. :)

Another recent hunt was for vintage/antique horse prints. That led me to a great site that sells original chromolithographs of all subjects. I bought the 1903 horse one they had and absolutely love it. I’m looking on there now for architectural or sea-life art. Link: https://www.stonegateprints.com

And if you have a piece you love already, see if the artist has other works and collect them. I’m doing that with Paulus Potter, among others — have a print and a giclee (my DH found through Amazon) of his so far.

Good luck!

I second Ida's suggestion of https://www.dailypaintworks.com. This is a splendid site! Aside from its great selection of artists, its other feature is that you can have an original painting for a very affordable price. So a beginning collector can test his/her taste for not a large investment. I have purchased from several of the artists. They are most accommodating; some of them will alter the size or color spectrum of a work that you like. One painting that I loved was sold just before I contacted the artist. She volunteered to paint another similar to it, even asking me if I would like anything changed. Yes, said I, could you make the woman's dress a deeper pink? And she did!

A word of caution: this site is highly addictive if you are exploring your taste and wanting to collect. There is so much to look at!

Another excellent source of art works are the many artist co-ops that dot the country. I've purchased pieces in Port Townsend WA, Tehachapi CA, and Green Valley AZ (just to let you know how ubiquitous these co-ops are).

Don't be intimidated! Buy what you like and keep on looking, looking, looking!

Sable

I just found out my favorite local frame shop and gallery has an Etsy shop where it looks like the unsold pieces from the gallery shows are put up for sale. She does a big tiki show every summer, which explains the current items on offer.

https://www.etsy.com/shop/CreativeArtForSale

Thanks for all of the recommendations. I have been slowly perusing the sites and didn't even think of Etsy, but that is a rabbit hole (for me) that requires more time or at least limiting my time when I do go there.