Sometimes it is good to make dangerous things, but only in VERY small quantities. It gives you an impression of how dangerous they actually are and that kind of knowledge is important.
So, I encourage a starter to make some chlorine, but only in VERY small amounts. Carefully sniffing gives you the smell of it, so you will recognize it, when you accidently make it in another experiment. The same is true for SO2, Br2, NO2. Make them in a test tube (using 100 mg of chems, not more) and carefully sniff them. Not by sticking your nose in the test tube, but by wafting some of the gas towards your nose with your hand. Really, it learns you a lot.
If I may suggest a set of chems, which are interesting, and which can all be purchased at a single shop (PM for info, I don't post addresses over here, and I decide whether I give the address or not based on post history), then I would suggest the following:
50 g KI
100 g KBr
100 g Na2SO3
100 g Fe(NO3)3.9H2O (better than chloride, the nitrate does not form a complex with ferric ion in aqueous solution)
100 g FeSO4.7H2O
100 g K2Cr2O7 (careful: carcinogen, but otherwise not really dangerous, but allows a LOT of really funny/colorful experiments in aqueous solution).
100 g KMnO4 (careful: very potent oxidizer, much more so than K2Cr2O7, only use in aqueous solutions when you are inexperienced).
100 g K2S2O8
100 g NaNO2 (this is my favorite, no other chemical is good for so many good aqueous chemistry experiments)
100 g NaSCN (nice complex formation with many metals)
100 g KCr(SO4)2.12H2O (chrome alum, funny and cheap)
100 g CuSO4.5H2O
100 g KOH (or NaOH)
250 g NaHCO3
250 g Na2S2O3.5H2O (good old hypo, dirt cheap, yet funny chem)
100 g Na2B4O7.10H2O (borax)
100 g K3Fe(CN)6 (potassium ferricyanide, non-toxic, despite the cyanide ligands, very versatile chem, good very many experiments)
100 g K4Fe(CN)6.3H2O (potassium ferrocyanide, idem)
50 g Na2S.xH2O (caution: makes H2S in contact with acids, but it is a nice versatile chem, which however, must be kept very well stoppered)
Some chems, which you should not spend money on if you are not a pyro-hobbyist:
Nitrates and perchlorates are very inert in aqueous solution, unless highly concentrated, or at extremely low pH (between -1 and 0). Sodium sulfate is as energetic as a dead dog and cannot react with anything. Not interesting at all.
Locally you should try to obtain
1 liter NH3 (5% is OK)
100 ml H2O2 (3% is OK)
1 liter HCl (30%)
1 liter H2SO4 (32%, battery acid, be careful with the 96% stuff, 32% is relatively safe)
100 grams TCCA (trichloro isocyanuric acid, swimming pool slow acting organic chlorine, unfortunately this mostly only is available in kilo-packages)
1 liter NaClO (4% is OK, common household bleach)
A few gallons of distilled water. This is the only chemical which I use in large quantities. I do all of my aqueous transition metal chemistry experiments in distilled water. Really, spend the money for this, it is worth it. If you buy it in jerrycan quantities it is quite cheap anyway.
HNO3 probably will be very hard to obtain in the USA. Over here in NL it is easy to obtain at 52% but I know that at the other side of the ocean things are quite different. It would be nice though if you could obtain that, but you do not need it to start with.
It really is best to obtain H2SO4, it is a very versatile acid, more so than HCl. The chloride ion coordinates to many transition metal ions and for many experiments that is not what you want. NaHSO4 is a very good and safe alternative and can be purchased locally as pH-minus for swimmingpools.
From a ceramics and pottery supplier you can obtain the following very interesting transition metal compounds for really low prices:
100 gram V2O5, vanadium pentoxide
100 gram CoCO3, cobalt carbonate (don't buy Co3O4, it is inert and does not dissolve in any solvent)
100 gram NiCO3.Ni(OH)2, (basic) nickel carbonate
100 gram CuCO3.2Cu(OH)2, (basic) copper carbonate
100 gram MoO3, molybdenum trioxide, makes molybdates easily with solutions of NaOH or KOH)
100 gram ZnO, zinc oxide
Another interesting chemical may be silver nitrate, AgNO3 (available from the same source as the chems, I mentioned above), but it is fairly expensive. You could consider buying 10 grams, but still, it costs $10 or more.
With the list, given here, you can do a LOT of aqueous chemistry experiments and also quite some nice (colored) gas experiments. All these experiments can be done safely, also at home, but of course, you should use your brains and not do stupid things. Always use small amounts (max. 100 mg, small spatula of solid, with a few ml of water or acid added to dissolve it). With that you simply won't have serious accidents, because quantities are too low to be really dangerous. The only organ which could be severely damaged with such small amounts is the eye, so wear glasses or goggles ALWAYS when experimenting.