Is it just the toilet, or are other things slow too - bath drain, sink drain? If it's just the toilet, I wouldn't think it's the septic system yet, usually if there is a bind up, everything behind the bind up tends to slow down.
*IF* you or DH is mechanically inclined, good at directions, and patient, removing and replacing a toilet is not hard. It's smelly, and gross, but not hard. There may be a plug in the trap of it that needs to be cleared. I've pulled toilets before-if you do pull it, you do want to get a new wax ring (cheap) to ensure a good seal.
I personally don't like snakes - they damage porcelain and some pipes really easily. I've used one before, and blown right through an old pipe, and had to rush at midnight to a 24 hour store to get all new plumbing and repair it.
One BIG thing I've learned - the absolute bane of plumbing systems is......tampons. If you or the women/girls in your household use them, you may want to consider wrapping and disposing them. I first got my taste of their problem when renting a house - I didn't use them but my roommate did, and EVERYTHING in the house drained slow one time. I used every drain clog known to man, that danged snake (busted the kitchen sink drain), everything. Finally had a plumber out, and close to the join in the sewer, there was a huge mass of them, effectively blocking everything. It was incredibly gross, and he suggested to never flush them - he had to clear them out more than anything else ever. If your system is in perfect condition, they can flush, but once tree roots grow in, and snags in the pipe show up, or anything, guess what - "white mice" city. They also do NOT degrade well - if you have a septic system in your yard, they will eventually cause problems there as well.
How to remove/replace a toilet:
How to Remove and Replace a Toilet | DoItYourself.com