I started my pico thinking that it would be a good way to get into SW without spending a lot of money.
I've spent a lot of money.
I've probably spent over $200 on my pico reef so far, and remember that I already had a bunch of LR and the Aquaclear filter so it would have been more otherwise. If cost really is a big factor for you, then maybe it isn't such a good idea. A nano tank also requires a lot of attention. Lots. I have to top off my pico with FW twice a day to keep the salinity stable, and I've been changing water every 2-3 days. If you have the money but not a lot of time, you may want to consider a larger tank, like 29 gallons or more. It's much easier keeping a larger tank stable than a smaller tank.
If you're really serious about wanting to do this, here is what I would consider buying.
a refractometer- this is really the only way to determine the SG of your water in any sort of accurate way. Hydrometers are pretty much junk, and a refracto is ABSOLUTELY worth the money.
decent lighting- if you want to start a reef, this is essential. What you buy, of course, will be determined by what size tank you get. A very general guideline is that 3 wpg or more will give you enough light to grow soft corals. Normal output lighting probably won't cut it either- you'll probably want to go with power compacts or T5's if your tank is large enough, but pc's come in a much wider variety of sizes. Keep in mind that your tank will probably end up open-top, so buy mounting legs for your light if they are available.
a powerhead- even if you set up a tiny tank like mine where you have enough turnover without a powerhead, you'll still need one for mixing up your SW.
aragonite sand- it's easier to keep clean than crushed coral.
live rock- 1-2 pounds per gallon.
either an RO unit or RO water, and RO/DI is even better- my tank is so small that I just take a jug and buy 2 gallons of RO at a time. Then I mix up my water at home.
salt mix- I use Oceanic. Asking what kind is the best is like asking what the best model of car is. Everyone has an opinion.
HOB filter- this isn't necessary I suppose, but especially in a small tank it will move a lot of water. Plus, you can take out all the media and cram the chamber full of LR rubble. This gives your tank more bio filtration.
a skimmer- depending on the size of tank you want, this may be a good idea. My tank is so small that I keep it in check with just water changes.
a heater- just like in FW, you want to keep your temp stable.
a SW test kit- this is extremely important, and your FW test kit won't work for SW.
Someone jump in here if I am forgetting anything.
Anyway, you can see how this could get expensive pretty quickly.
I'm not trying to discourage you at all, just pointing out that it will not be a low cost or low maintenance endeavor.