Easiest Coin Series To Collect?

Some of the variety and error sets of common coins are challenging, but possible from circulation or with some junk box searching.

Consider these:
"BIE" Lincoln Cents 1934 P-D-S to 1958 P-D (I don't know of anyone who has a complete set. It's much tougher than you may expect)
Wheat stalk die chip Lincoln Cents 1934 P-D-S to 1958 P-D (this one can be done)
At least one minor DDO or DDR for each of the dates and mints of Lincoln Cents 1934 P-D-S to 1958 P-D (this will require all three major die variety site listings to complete, but it can be done)
Plugged LIBERTY or date Lincoln Cents 1934 P-D-S to 1958 P-D (it will take some flexibility, but can be done. The plugged "B" and skirted "R" combined with plugged "9" and "5" and "6" coins likely will be needed).

The 1943 P-D-S cents won't be found in circulation, but can be found easily in dealer junk boxes. Other options exist, including the "cracked skull" and "spiked head" coins, excessively polished dies sets (1934 is a bonanza year), pre-cuds / Retained Cuds, or all with clipped planchets or all with rotated dies, and so on.

If you want a tough challenge, try a 1934 P-D-S to 1958 P-D Lincoln Cent set all in the same circulated grade (if you are adventurous, try VG-F) or all all with the nice even chocolate color (1943 P-D-S is obviously excluded from this set).

Well played.

My opinion—and I could be wrong—is that the Roosevelt dimes will be easier than the Washington quarters. The dime gets little love and I believe the different quarter programs drove a significant number of the original design quarters out of circulation.

That being said, I would defer to cladking's opinion over mine.