I am looking to purchase gear to get my certification and for an upcoming trip.
This suggests you are looking well beyond the 'personal' gear - mask, fins, snorkel, boots - and includes regulator, BCD, exposure suit, etc.
Would purchasing it at the same place I take lessons at be a wise decision
It is probably wiser to work through the store where you are taking lessons, IF you plan to have a continuing relationship with them after certification. If you picked a LDS simply because they happen to offer a course at the particular time you need it, but it is very unlikely you would continue to use them (they are a 60 minute commute away from where you live/work, or you already don't care for the atmosphere, whatever), then the answer is 'probably not'. If you picked them for convenience, or their friendly, welcoming approach to you as a new diver, and you anticipate continuing to do business wth them in the future, then the answer is 'probably would'.
or should I look for equipment myself
I usually don't recommend that new / uncertified divers purchase equipment themselves, without any input from more experienced divers or instructors. You can do it, you are free to do lots of research, to consult with unknown electron emitters (like me) on SB, to spend your money as you see fit. But, I wouldn't recommend what would essentially be a blind purchasing decision. Part of the value of a LDS is supposed to be the personal interaction and, ideally, the experience and (dare I say it) 'wisdom' that you should get as part of the purchase price.
I have seen a number of cases where people bought essentially an entire rig - exposure suit, BCD, regulator, even a dive computer - along with the personal items, BEFORE strating their OW class, because they wanted to train in what they would use during and after certification, and/or they had a scuba trip planned immediately after certification. Our LDS actually discourages that at the OW level (gently, with comments such as, 'We very much want to help you with your first gear purchases. You might find it helpful to get started in the class with the equipment we use with students, and then come back right after you finish, before you take your trip, and we'll work with you to get you outfitted.') But, we will not refuse a sale to a committed customer. Sometimes, in those cases we and the customer are simply lucky - we put them in gear that turns out to be very well-suited to their post-certification needs. Sometimes, it does not work out. In one case I remember, one of two divers (of a husband/wife pair that bought complete rigs before starting training) never made it through certification, and the spouse was left with two sets of somewhat expensive, essentially new, but now 'used' gear, that would not be used by them again.
I'm wondering if the store I'm taking lessons at will have the best equipment or if it will be marked up quite a bit.
That is difficult to answer on SB, for two reasons. 1) What constitutes 'best equiipment' is quite subjective. Most shops carry several major brands, certainly not all. And, most major brands provide a spectrum of equipment choices, from simple, but functional and inexpensive, all the way to unnecessarily 'trinket-ized' and overpriced. The 'best equipment' for you is ultimately what you find to be most comfortable and functional - its fits YOU well, it provides the functionality YOU need, etc. And, as others have already said, you need to gain some experience in the water before you know what YOUR needs are. 2) Each LDS will have a mark-up. But, business practices differ substantially among shops. I would not expect every LDS to match LP or Scubatoys prices. That doesn't mean that the lowest price is the best criteria for value, either. Nor, do I expect shop prices to be 2 (or 3, or 4) times what the larger online vendors may charge. I am a LDS supporter, I have received enormous value from my association over the years, and I believe that a good LDS is worth every penny they charge. But, I know that every LDS is not the same.
A good starting point - speak to the staff in the store through which you are taking lessons. If they immediately take the 'I know exactly what you need, and we have the ideal package for you right here' approach, run away, very fast. On the other hand, if they offer thoughtful comments, ask questions about YOU, and what you think you might want, and suggest that you might want to spend some time in the water before plunging into gear purchases, then they might be a LDS worth doing business with.
elan:
All my gear that I have purchased before the course, except the reg is now sold and I'm now diving completely different setup, if only I had known about this forum before I would not had purchased a lot of things that I had to sell later.
And, this experience is not uncommon. Part of the reason is that we have little / no power of discrimination as a novice, and are led (or misled) into purchases that don't suit our needs. But, in fairness to all, at least part of the reason that our first equipment purchases often end up being sold, and new equipment purchased, is that our needs evolve as we develop as divers. My first BCD was a Zeagle Ranger, bought within 6 months of certification. I still have it 10 years later, but haven't dove it in 5 years at least. It is a GREAT BCD. I loved diving it. But, I evolved to a different rig as my diving interests expanded, or became possibly more focused. I don't regret the decision. But, if I had to do it again I might have asked about a BP/W, for example.