Here are the comics I know I definitely bought in June of 1981:
DC Comics Presents 34 featuring Superman and Captain Marvel. While my first exposure to the character was probably the live-action Saturday morning TV series, I can't remember when I first encountered the comic book version of Captain Marvel. My first memory was of a giant, treasury-sized edition with a photo cover that my dad would have bought for me on a rare (and therefore special) trip to Toys 'R' Us. I believe it featured a big story pitting the Marvel Family against the evil mad scientist Dr Sivana and his family, and a photo cover of Jackson Bostwick from the (possibly then-current) live-action TV series.
Again, reaching back into my memory, I'm pretty sure that Toys 'R' Us was a good distance away from our house, and we stopped there on our way to some rail fan thing my dad was taking me to. I read the whole comic on that trip. It was such a great story, drawn so well (probably by C.C. Beck) that I had to have more. At the time, "having more" meant acquiring stories when the opportunity arose, rather than actively seeking them out, so while I did eventually acquire a copy of Shazam: From the 40s to the 70s from the bargain table of the book department of Capwell's Department Store, I completely missed the regular Shazam series from DC.
So this issue of DC Comics Presents was special. It was my first opportunity to pick up a new Captain Marvel story off the stands, as it came out. Plus, it was my first exposure to Hoppy, the Marvel Bunny, which really amused me. Since so many of my early comics were funny animal books, this comic was like a bridge for me. (And it got me ready for the first appearance of Captain Carrot, less than a year away.)
Marvel Premiere 60, the final Doctor Who issue, featured a painted cover by Earl Norem that captures the spirit of the show, but still doesn't look quite right to me. It's still eye-catching, though; more so back in those days when painted covers were few and far between. I remember my disappointment when I got to the end and saw that the next issue would be featuring Captain Universe (I believe), not Doctor Who. However, at this point, I was already getting in the habit of poking my head in my local comic book store on at least a semi-regular basis.
Tales of the Green Lantern Corps 2 continues what I enjoyed about the first issue. Despite the recent reprinting of this series, I haven't read it in years, so I can't remember any specifics about this issue on its own. However, looking at the other comics that came out this month, I see that if my enjoyment of this series had gotten me to buy the regular Green Lantern series at the time, I would have started reading just at the time the Omega Men made their first appearance. Given that I became a bit of an Omega Men fan from their appearances in Teen Titans and their own book, I'm kicking myself a little bit for not at least checking out Green Lantern at this point.
However, at the time, comics still weren't something I bought on a regular basis, or so I told myself. Oh, how things would change!