This is in the top five of most asked questions on here and same advice as always year on year!
Look on eBay (local ads/ Gumtree, Boats and Outboards etc) for a nice used 3.2m to 3.6m SIB outfit with engine included - preferably a 9.8 or 15hp 2 stroke from one of the big makes - Tohatsu, Suzuki, Mariner/Mercury, Yamaha. Contact the seller as soon as it is listed, view it personally and barter with cash - don't get involved in bidding wars or buying sight unseen.
Stick to an established SIB make - Zodiac, Honwave, Quicksilver, Suzumar, Tohatsu.
Buying this way and going with big established and known brands that hold their value gives you by far the best bang for your buck.
An endless sucession of outfits like this are listed each week - buy one in good condition that someone has seen at a nice boat show, thought 'I fancy that', subsequently not enjoyed the whole hassle/boating thing and therfore taken the original big depreciation hit on.
Budget around £1500 to £1800 for the above. You may often get a trailer included too which can be sold on if not needed.
Buy separately and you're looking at (used and same big name items) - SIB around £500/600, engine around £1200, trailer around £250.
Look after it and you will not lose any money if you re-sell.
Obviously with patience, looking hard, being lucky and maybe not being so fussy on condition/age you can find stuff *much* cheaper than this.
The engines menetioned above (particularly the later mid 2000 models) continue to rise in value not fall.
Obviously you will need a few extras, lifejackets/anchor etc but more often than not you will get these thrown in with the outfit.
This is an example - it's actually a 4 stroke but might suit you better for trolling - I had one of these 380 Tohstsu's and they are big with a really solid proper boat feel - hard floor also great for fishing gear.