You could get one of those saddle pads with the pockets like this https://www.amazon.com/CHALLENGER-Quilted-Australian-English-Dressage/dp/B07KYXCBKD/ref=asc_df_B07KYXCBKD?tag=bingshoppinga-20&linkCode=df0&hvadid=80539307115998&hvnetw=o&hvqmt=e&hvbmt=be&hvdev=m&hvlocint=&hvlocphy=...
Poundo board. $16.99. I've had mine for 2 years.
I like this Pro Tec pad and use it on several bags: https://www.amazon.com/Pro-Tec-Neoprene-Shoulder-SHPAD12/dp/B00UFCVK8O/
Ultimately, crossbody/one strap carry is best with light loads only for all day use. If you’re carrying more than a few pounds it’s backpack time.
Until you can get your saddle fitted, how about one of these pads? They have inserts so one side can be pad-free while the other side padded. I have several of these and they’re great.
ECP Correction All Purpose Contoured Saddle Pad with Memory Foam Pockets https://www.amazon.com/dp/B06XH1R95W/ref=cm_sw_r_cp_api_glt_i_QA0NKSHFBGHVWF06RR07?_encoding=UTF8&psc=1
Oh wow, so many directions you could go. What's the riders color scheme? Could get something with an accent in that. Do they live in a warm climate? Maybe get something with cooling air flow sections. I'm sure people have favorite brands and whatnot but I always bought based on fluffiness and color.
This was the fluffiest pad I used for shows:
https://www.amazon.com/dp/B003MYCZH2/ref=cm_sw_r_awdo_navT_g_4CYK91Z1HG7EX774ZW54?psc=1
I even gave my extra one to a friend after my horse retired and she LOVES the pad too.
I’ve seen bareback pads this a little strap on the front that you can grab if you loose your balance or if your horse gets sassy! Here’s one I’ve used before