I was going to get Precheck, but I noticed that Global Entry is only slightly more money.
Do all the perks of TSA Precheck come with Global Entry or would they have to be purchased separately?
Yes. If you are approved for Global Entry (the standards around criminal history are more stringent than for Precheck alone), you will receive a Known Traveler Number that you may supply with your airline reservations and you will be eligible for Precheck (assuming you're flying a participating airline, at a participating airport, and you aren't randomly selected for more intense screening). It will work the same as if you applied for TSA Precheck.
Applying for Global Entry requires that you be interviewed by CBP at their centers, which are different locations from the TSA Precheck enrollment centers. Global Entry reserves the right to disqualify you for basically any criminal history or even just a fishy history with CBP, while TSA Precheck follows a more constrained set of rules where even pretty serious offenses are ok if enough time has passed. People have had all sorts of problems with Global Entry applications, though many are obviously accepted without incident. If you are denied for Global Entry, you won't get either Global Entry or TSA Precheck and will be out the application fee, requiring you to apply again just for TSA Precheck if you qualify for that.
Note also (with thanks to James McLeod in comments) the existance of the NEXUS program, which includes both Global Entry and TSA Precheck benefits along with expedited entry into Canada. Best of all, it only costs $50 for five years. The catch is that you can only enroll at limited locations near the US-Canada border, and the eligibility requirements are a bit different (must be a US or Canadian citizen or permanent resident). There's a handy comparison chart of all the trusted traveler programs you can consult to decide which is best for you. Weirdly, according to the chart, Canadian permanent residents will not receive TSA Precheck with NEXUS though.
For an authoritative source:
If you are a member of Global Entry (GE), you do not need to sign up separately for TSA's PreCheck program. TSA PreCheck is an added no-cost benefit offered to members of Global Entry, when passport and fingerprints are on file in our systems.
Note that your Global Entry application, passport, and airline reservations all must use the same name for this to work.
Personally, I'd go for Global Entry unless getting to an enrollment center was inconvenient or you have a concern that you might not be approved and don't want to risk wasting the money or time.
After you are approved for either Global Entry or Nexus or both (or any other trusted traveler program) you can add those cards in their GOES online system and then any of them can be used as proof of your TTP, in addition to the Known/Trusted Traveler number.