The two types of foreclosures, bank foreclosure and tax foreclosure, are generally handled very differently.
With a bank foreclosure (REO), the bank has taken back ownership of the home and will typically verify that the home has clear title (no liens or encumbrances) before selling the home to a new buyer. Banks will usually hire a local Realtor to manage the property and list it for sale on the local MLS service. Once the home is listed on the MLS, you should be able to have access to the house for a visual inspection. There will likely be some delay between the actual foreclosure date and the date that the property appears on the MLS, since the bank will need to have appraisals and BPO's (broker price opinions) in hand before determining price, make sure they have clear title, and they may need to evict the current occupants. REO's can be in various states of disrepair, with some being virtually move-in ready and others being completely trashed. Sometimes the bank will address these repair issues, but most of the time these homes are sold "as-is" with the buyer being responsible for all repairs.
With a tax sale, the first thing to verify is whether the tax sale passes full ownership to the new buyer, or if it is a sale giving you the right to earn interest on the unpaid taxes. You'll also need to verify whether there is a waiting period before you are sure you have ownership, and understand what happens if the current owner disputes the tax sale. Typically tax sale properties do not pass to the new owner free of all liens and encumbrances, so check for delinquent HOA fees and other items that could become your responsibility if you take ownership of the property. Also, tax sale properties are not "for sale" like a regular MLS listing, so you'll not be able to go inside and check it out, and you're not allowed to disturb the current occupants. Assume the worst with these homes, and expect that you'll need to replace cabinets, flooring, sinks, toilets and appliances at a minimum.
Remember that the list price of homes being sold as foreclosures is just a starting point. Quite likely they'll get bid up closer to the current market value for your area, unless there are some circumstances that make that home less desireable than the rest of the neighborhood. Tax sales are typically done in an auction environment, with people bidding against each other, investors against regular homebuyers. Bank owned (REO) homes with multiple offers will turn into a bidding war as well, but you generally won't have everyone in the same room as in an auction - you'll be submitting "best and final" offers instead.
Finally, you'll need to determine how you can finance your home purchase. With a bank owned (REO) home, you can usually obtain standard financing through a local lender and take up to 30-45 days to complete your financing and transfer ownership. With a tax sale, you won't always have the luxury of time, and you won't always be able to get traditional financing. Tax sales will either want a percent of the purchase price up front and the balance within a designated timeframe, or they'll want the full price up front. Since they typically don't guarantee clear title, it may not be possible to obtain standard bank financing on a tax sale.
All things considered, there are generally fewer risks in purchasing a bank owned (REO) home than buying a home at a tax sale. The REO should provide clear title, allow time for conventional financing, and allow for physical inspections before you're required to complete your purchase.