I would recommend checking out Batt's Go Picks. There are 10 sets at the moment, so plenty of games and he tends to pick ones that are easy for amateurs to follow. They are usually exciting games and I've loved studying them myself.

Here is the most recent episode: Batt's Go Picks #10

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"You have to walk before you can run. Black 1 was a walking move.
I blushed inwardly to recall the ignorant thoughts that had gone through
my mind before, when I had not realized the true worth of Black 1."
-Kageyama Toshiro on proper moves

The answer is whoever you want to. Studying any strong players will be useful. Studying modern pros will be more useful for joseki at least, but I don't think that should deter you from studying any players you like.

The important thing is to enjoy the games. I like having in depth commentary like you can get from gogameguru.com.

I think the best thing you can do is play through a few games from several different pros and see if there's a particular style/player who really appeals to you. It'll be much easier to study games if you really enjoy following them and liking the moves.

Personally I really love the endgame mastery of players like Lee Changho and Park Yeonghun; they make it seem almost effortless, playing an easy game and always just staying one point ahead. It's like watching a magic trick somehow. (Park Yeonghun is probably my favorite pro, although he hasn't been winning as many things lately).

Sensei's Library has a (probably inaccurate and outdated) list of pro players styles that you might find interesting to browse:
http://senseis.xmp.net/?ProfessionalPlayersGoStyles

Any player will do.

After replaying quite a few pros I can say that my favourite players are Honinbo Dosaku and Shuei, Go Seigen and Chen Yaoye. I always get excited when replaying their games. And as others have mentionend, that's the key.
So, really, start anywhere you like, it doesn't really matter as long as you do : )

I wouldn't recommend ancient chinese like Huang Longshi or korean players, though, because they start with a complete different opening layout.

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My "guide" to become stronger in Go

I love Dosaku's games as well, but... They are always so hmm... messy!? How do you make sense of what's actually going on?

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Geek of all trades, master of none: the motto for my blog mostlymaths.net

How do I ever make sense of pro games? =D I just let me mesmerize.

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My "guide" to become stronger in Go

For a beginner, I suggest focusing on players with a more solid/steady style. Any of the following fit this criteria, and you can find more.

Yasui Chitoku
Honinbo Shuwa
Honinbo Shusaku
Suzuki Tamejiro
Hayashi Yutaro
Sekiyama Riichi
Takagawa Kaku
Shimamura Toshihiro
Cao Dayuan
Shao Zhenzhong
Zhou Heyang
Yamada Kimio
Yi Ch'ang-ho (1993-2001)
Pak Yeong-hun
Kang Tong-yun
Chen Yaoye

As for studying go from different periods I think there are many things you could consider. But I'd like to mention just one main similarity and two main differences.

All periods have their own foundations -- openings and early middle game ideas -- from which their go is built and their games unfold. You'll have to learn the foundations from whichever period you study. In this regard, you can choose players from any period.

One difference is that older periods have a more narrow foundation, while newer games can call back to old ideas and use their current ideas. This makes learning older periods easier, because you're focusing on a more narrow slice.

A second difference is that recent periods have a more relevant foundation to modern and contemporary play. This makes playing against the majority of current players and following current professional games easier.

I will be looking at these. I'm beginning to believe that, at least for the beginner with some experience in playing actual games and solving problems in fuseki, jōseki, and chūban (as well as shikatsu and tesuji), replaying games by modern pros can be very informative.
I know that the games of Shūsaku and Dōsaku were played during a historical period in which komi was not given to White, so holding Black was advantageous and White had to be aggressive in her global development. Now that White gets komi, it is Black who has to be aggressive in global development. As well, the taisha, avalanche, and other large-scale jōsekis typical of 1800s and early 1900s Go are not in common use nowadays.

So, if I am not wrong, this means that - at least in the case of the serious student - it is not absolutely necessary to begin one's study of Go with games by historical players, but rather it is good, maybe better even, to replay and study games by modern pros?

From what I remember, Go Seigen once replayed the entire collection of Shūsaku's games as known back in the 1920s. This allowed him to understand the way Go was played in Japan at that time; the forms typical of Shūsaku's time were still the norm back then. Would it still be possible to glean anything useful from Dōsaku's and Shūsaku's games, even though hardly anyone plays in that style any more? Go Seigen has had immense influence on the development of Go after World War 2, so his games are a must for anyone studying modern styles of play.

I would not take this as any sign that Edo-era Go styles are making a comeback, but I believe this might be of interest to those reading here.

http://gosensations.com/?id=2&server_id=1&new_id=1227

Well, I have to say that I never really enjoyed studying pro games. Sure, I've played through lots of them, but not really studied them. So I don't know that it is essential unless your goal is 7d or above.

I would say to find a player whose style appeals to you and play through those, absorbing as much as you can. Then, after a few years pick another player with a different style. My favorite was always Sakata, but I am sure that is not to everyone's taste.

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Still officially AGA 5d but I play so irregularly these days that I am probably only 3d or 4d over the board (but hopefully still 5d in terms of knowledge, theory and the ability to contribute).

No one has mentioned what I find to be the most basic point of advice - don't pick players, pick openings. If you are currently trying to focus on one or two openings (like Orthodox or Chinese) or opening ideas (like 3-3), either keep an eye out for games with that opening or do a pattern search to download some. You'll find it easier to wrap your mind around the fuseki because you've seen some of the ideas before, you'll get to develop what you see because you'll get to put the opening into practice between studying games, and you'll get to the point of having actual insights about various moves more quickly. IMHO.

I only offer this as personal opinion.

When I started, it became clear to me quite quickly that I couldn't understand 95% of what was going on in a pro game. Despite this, I memorized a few of Shusaku's games (it had been pointed out in HnG that he was the best of the best ) and simply played them through and tried to get the feel for the 'flow of stones' (again, HnG-induced).

As it turns out, I soon began to beat my friends by ridiculous margins in our games. As it turns out, I did unconsciously learn a bit about 'direction of play' and important/unimportant areas, big and small moves, etc. Mostly, I learned to play with much better shape. Shape being a factor in efficiency (and therefore in winning), it ended up helping a lot. I feel I still carry the advantage this original 'push' to this day.

Just an idea.

Honestly, I don't think it matters. The beginner won't understand the games of either, never mind the concepts contained within. What you're looking to do, like Phoenix is talking about, is to internalise good shape, get a feeling for big areas vs small areas and other such *unconscious* processes. You'll get those from studying any very high level game. You won't on the other hand really "learn how to use outward influence" because sure while you can see the move they made but you won't be able to read out why that move was the right move there. It's the same with the joseki, sure you can see the complex joseki played out but you're unlikely to know why they picked that particular variation. Commented games are good for the latter simply because someone much stronger than you has done the reading for you.